RISC Publications and Technical Reports of Peter Paule
2024
P. Paule, C. Schneider.Creative Telescoping for Hypergeometric Double Sums. Technical report no. 24-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).January2024.arXiv:2401.16314 [cs.SC]. Licensed under CC BY 4.0 International.[doi][pdf][bib]
2023
Peter Paule.Ramanujan and Computer Algebra. In: Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence, K. Alladi, G.E. Andrews, B. Berndt, F. Garvan, K. Ono, P. Paule, S. Ole Warnaar, Ae Ja Yee (ed.), pp. -.2023.Springer,ISBN x.[pdf][bib]
Toufik Mansour and Peter Paule.Interview with Peter Paule.Enumerative Combinatorics and Applications ECA 3:1(#S3I1), pp. -.2023.ISSN 2710-2335.[doi][bib]
Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, Carsten Schneider.Error bounds for the asymptotic expansion of the partition function.Rocky Mt J Math to appear, pp. ?-?.2023.ISSN: 357596.arXiv:2209.07887 [math.NT].[doi][bib]
G.E. Andrews and P. Paule.MacMahon's Partition Analysis XV: Parity. Technical report no. 23-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2023. Licensed under CC BY 4.0 International.[doi][pdf][bib]
G.E. Andrews, P. Paule.MacMahon's Partition Analysis XIV: Partitions with n copies of n.To appear in: Journal of Combinatorial Theory, Series A(22-14), pp. -.2023.???.[doi][bib]
2022
K. Banerjee, P. Paule, C. S. Radu, W. H. Zeng.New inequalities for p(n) and log p(n). Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6607, 2022.To appear in the Ramanujan Journal.[pdf][bib]
2021
Peter Paule (ed.), Stephen Melczer.An Invitation to Analytic Combinatorics.Texts and Monographs in Symbolic Computation1st edition,2021.Springer,978-3-030-67080-1.[bib]
Peter Paule, Cristian-Silviu Radu.Holonomic relations for modular functions and forms: First guess, then prove.International Journal of Number Theory17(3), pp. 713-759.2021.World Scientific,1793-0421.[doi][bib]
Ralf Hemmecke, Peter Paule, Silviu Radu.Construction of modular function bases for $Gamma_0(121)$ related to $p(11n+6)$.Integral Transforms and Special Functions32(5-8), pp. 512-527.2021.Taylor & Francis,1065-2469.[doi][bib]
Peter Paule.Contiguous Relations and Creative Telescoping. In: Anti-Differentiation and the Calculation of Feynman Amplitudes, J. Bluemlein and C. Schneider (ed.), Texts and Monographs in Symbolic Computation, pp. 335-394.2021.Springer,ISBN 978-3-030-80218-9.[doi][pdf][bib]
George E. Andrews and Peter Paule .MacMahon's partition analysis XIII: Schmidt type partitions and modular forms.Journal of Number Theory, pp. 95-119.2021.Elsevier,ISSN 0022-314X.[doi][pdf][bib]
Peter Paule, Cristian-Silviu Radu.An algorithm to prove holonomic differential equations for modular forms. In: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019., Bostan A., Raschel K. (ed.), Springer Proceedings in Mathematics & Statistics373, pp. 367-420.2021.Springer, Cham,978-3-030-84303-8.[doi][bib]
K. Alladi, B.C. Berndt, P. Paule, J.A. Sellers, A.J. Yee.George E. Andrews 80 Years of Combinatory Analysis.Trends in Mathematics1st edition,2021.Birkhaeuser,Cham,ISBN 978-3-030-57050-7.[doi][bib]
2020
Peter Paule, Cristian-Silviu Radu.An algorithm to prove holonomic differential equations for modular forms. Technical report no. 20-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).May2020.A final version appeared in: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2029, eds.: A. Bostan and K. Raschel, Springer, 2021. Licensed under CC BY 4.0 International.[pdf][bib]
Peter Paule (ed.), Tetsuo Ida.An Introduction to Computational Origami.Texts and Monographs of Symbolic Computation1st edition,2020.Springer,978-3-319-59189-6.[bib]
Peter Paule, Silviu Radu.Holonomic Relations for Modular Functions and Forms: First Guess, then Prove. RISC. Technical report no. 20-14, 2020.[bib]
2019
P. Paule, C. Schneider.Towards a symbolic summation theory for unspecified sequences. In: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, P. Paule, C. Schneider (ed.), Texts and Monographs in Symbolic Computation, pp. 351-390.2019.Springer,ISBN 978-3-030-04479-4.arXiv:1809.06578 [cs.SC].[doi][pdf][bib]
Peter Paule, Silviu Radu.A UNIFIED ALGORITHMIC FRAMEWORK FOR RAMANUJAN'S CONGRUENCES MODULO POWERS OF 5, 7, AND 11. Technical report no. 19-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).submitted,2019.[pdf][bib]
Peter Paule, Silviu Radu.A proof of the Weierstrass gap theorem not using the Riemann-Roch formula.Annals of Combinatorics23(19-02), pp. 963-1007.May2019.Springer,0218-0006.[doi][bib]
2018
Christoph Koutschan, Peter Paule.Holonomic Tools for Basic Hypergeometric Functions. In: Frontiers of Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. 393-416.2018.World Scientific Publishing,ISBN 978-981-3228-87-0.[doi][pdf][bib]
Peter Paule, Cristian-Silviu Radu.Rogers-Ramanujan functions, modular functions, and computer algebra. In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider, E. Zima. (ed.), Springer Proceedings in Mathematics & Statistics226, pp. 229-280.2018.Springer, Cham,978-3-319-73231-2.[doi][pdf][bib]
2016
Manuel Kauers, Peter Paule, Greg Reid.Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra.ACM Communications in Computer Algebra50(Issue 1), pp. 27-34.March2016.1932-2240.[pdf][bib]
Peter Paule, Cristian-Silviu Radu.A new witness identity for $11|p(11n+6)$. In: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, George E. Andrews, Frank Garvan (ed.), pp. 625-640.2016.Springer, 2194-1009.[pdf][bib]
Peter Paule, Silviu Radu.Partition analysis, modular functions, and computer algebra. In: Recent Trends in Combinatorics, IMA Volume, A. Beveridge, J. R. Griggs, L. Hogben, G. Musiker, P. Tetali (ed.), The IMA Volumes in Mathematics and its Applications159, pp. 511-543.2016.Springer, Cham,978-3-319-24296-5.[doi][pdf][bib]
2015
Peter Paule, Silviu Radu.Partition Analysis, Modular Functions, and Computer Algebra. Technical report no. 15-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).In Recent Trends in Combinatorics, IMA Volume 511-543,2015. Licensed under CC BY 4.0 International.[pdf][bib]
2014
Christoph Koutschan, Peter Paule, Sergei K. Suslov.Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II. In: Algebraic and Algorithmic Aspects of Differential and Integral Operators, Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz (ed.), Lecture Notes in Computer Science8372, pp. 135-145.2014.Springer,Berlin Heidelberg,ISBN 978-3-642-54478-1.[pdf][bib]
2013
Peter Paule, Sergei K. Suslov.Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.. In: Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013, Carsten Schneider, Johannes Blümlein (ed.), pp. 225-241.2013.Springer,978-3-7091-1615-9.[bib]
S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann.Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation, pp. 75-96.2013.Springer,ISBN-13: 978-3709116159.arXiv:1305.4818 [cs.SC].[doi][pdf][bib]
Peter Paule.Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift.1st edition,2013.Springer,978-3-319-00965-0.[bib]
2012
Peter Paule, Cristian-Silviu Radu.The Andrews-Sellers family of partition congruences.Advances in Mathematics230(3), pp. 819-838.2012.0001-8708.[doi][pdf][bib]
Peter Paule, Sergei K. Suslov.Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I. Technical report no. 12-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).2012.Published in: Computer Algebra in Quantum Field Theory Integration, Summation and Special Functions, Buchreihe: Texts & Monographs in Symbolic Computation, Verlag: Springer Vienna, Print ISBN: 978-3-7091-1615-9..[pdf][bib]
George E. Andrews and Peter Paule.MacMahon's Dream. In: Partitions, q-Series, and Modular Forms, K. Alladi and F. Garvan (ed.), Developments in Mathematics23, pp. 1-12.2012.Springer,978-1-4614-0028-8.[bib]
2011
Manuel Kauers, Peter Paule.The Concrete Tetrahedron.Text and Monographs in Symbolic Computation1st edition,2011.Springer Wien,978-3-7091-0444-6.[bib]
P. Paule, V. Pillwein.Automatic Improvements of Wallis' Inequality. In: SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida and others (ed.), pp. 12-16.2011.IEEE Computer Society,0.[pdf][bib]
2010
Peter Paule, Silviu Radu.Infinite families of strange partition congruences for broken 2-diamonds .The Ramanujan Journal23, pp. 409-416.2010.1382-4090.[doi][pdf][bib]
Peter Paule.Henrici's Friendly Monster Identity Revisited. In: "Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008, Kotsireas, Ilias S.; Zima, Eugene V. (ed.), pp. 155-163.2010.Springer,978-3-642-03561-6.[bib]
F. Chyzak and P. Paule.Chapter Computer Algebra. In: NIST's Digital Library of Mathematical Foundations, F. Olver et al. (ed.), pp. 0-0.2010.0.[bib]
2009
Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler.Algorithms in Symbolic Computation. In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62.2009.Springer,978-3-642-02126-8.[doi][pdf][bib]
Peter Paule, Silviu Radu.A Proof of Sellers' Conjecture. RISC. Technical report no. 09-17, 2009.[pdf][bib]
Peter Paule.The Renaissance of Algorithmic Mathematics. In: Hagenberg Research, Peter Paule (ed.), pp. 6-15.2009.Springer Berlin-Heidelberg,978-3-642-02126-8.[bib]
2008
William Y. C. Chen, Peter Paule, Husam L. Saad.Converging to Gosper's Algorithm. Technical report no. 08-20 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2008.Published in: Advances in Applied Mathematics Volume 41, Issue 3, September 2008, Pages 351-364..[pdf][bib]
Peter Paule.Henrici's Friendly Monster Identity Revisited. Technical report no. 08-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December2008.Dedicated to Professor Georgy Egorychev on the occasion of his70th birthday. Published in: Advances in Combinatorial Mathematics pp 155-163, Springer..[pdf][bib]
William Y. C. Chen, Peter Paule, Husam L. Saad.Converging to Gosper's Algorithm.Adv. in Appl. Math.41(3), pp. 351-364.2008.0196-8858.[bib]
2007
F. Chyzak, P. Paule.Computer Algebra. In: The Digital Library of Mathematical Functions (DLMF), D. Lozier (ed.), pp. n/a-n/a.2007.National Institute of Standards and Technology (NIST),Gaithersburg, U.S.A.,electronic.In preparation.[bib]
Manuel Kauers, Peter Paule.A Computer Proof of Moll's Log-Concavity Conjecture.Proceedings of the AMS135(12), pp. 3847-3856.December2007.ISSN 0002-9939.[ps][bib]
P. Paule, C. Schneider.Truncating Binomial Series with Symbolic Summation.INTEGERS. Electronic Journal of Combinatorial Number Theory7(A22), pp. 1-9.2007.ISSN 1553-1732.[url][pdf][bib]
George E. Andrews, Peter Paule.MacMahon's Partition Analysis XI: Broken diamonds and modular forms.Acta Arith.126, pp. 281-294.2007.ISSN 0065-1036.DOI: 10.4064/aa126-3-5.[bib]
G. E. Andrews and P. Paule.MacMahon's Partition Analysis XII: Plane Partitions.Journal of the London Mathematical Society76(3), pp. 647-666.2007.London Mathematical Society,0024-6107.[bib]
G.E. Andrews and P. Paule.MacMahon's Partition Analysis XI: The Search for Modular Forms.Acta Arithmetica 126, pp. 281-.2007.0.[bib]
2006
G. E. Andrews, P. Paule.MacMahon's Dream. SFB 013. Technical report, September2006.SFB-report 2006-26. Published in: Partitions, q-Series, and Modular Forms pp 1-12, Springer..[pdf][bib]
G. E. Andrews, P. Paule.MacMahon's Partition Analysis XI: The Search for Modular Forms. SFB 013. Technical report, 2006.SFB-report 2006-27.[pdf][bib]
G. E. Andrews, P. Paule.MacMahon's Partition Analysis XII: Plane Partitions. SFB 013. Technical report, September2006.SFB-report 2006-28. Published in: Journal of the London Mathematical Society, Volume 76, Issue 3, 1 December 2007, Pages 647–666, https://doi.org/10.1112/jlms/jdm079..[pdf][bib]
A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, J. Schoeberl.Hypergeometric Summation Algorithms for High Order Finite Elements.Computing78(3), pp. 235-249.2006.ISSN 0010-485X.Preliminary version available.[doi][pdf][ps][bib]
P. Paule, V. Pillwein, C. Schneider, J. Schöberl.Hypergeometric Summation Techniques for High Order Finite Elements. In: PAMM, , Proceedings of GAMM Annual Meeting 2006 - Berlin6/1, pp. 689-690.2006.Wiley InterScience,Weinheim,ISBN.[doi][bib]
2005
G. E. Andrews, P. Paule, C. Schneider.Plane Partitions VI: Stembridge's TSPP Theorem.Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud34(4), pp. 709-739.2005.ISSN 0196-8858.Preliminary version online.[doi][pdf][ps][bib]
2004
G.E. Andrews, P. Paule, C. Schneider.Plane Partition VI: Stembridge's TSPP Theorem -- A detailed algorithmic proof. Technical report no. 04-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).May2004.[pdf][ps][bib]
G. E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis XI: Hexagonal Plane Partitions. J. Kepler University Linz. Technical report no. 2004-4, March2004.SFB-Report.[pdf][bib]
G. E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis X: Plane Partitions with Diagonals..Southeast Asian Journal Mathematics and Mathematical Sciences3, pp. 3-14.2004.ISSN 0972-7752.[pdf][bib]
2003
P. Paule, C. Schneider.Computer proofs of a new family of harmonic number identities.Adv. in Appl. Math.31(2), pp. 359-378.2003.ISSN 0196-8858.Preliminary version online.[doi][ps][pdf][bib]
P. Paule, V. Strehl.Definite Summation and Hypergeometric Identities. In: Computer Algebra Handbook: Foundations, Applications, Systems, J. Grabmeier, E. Kaltofen, V. Weispfenning (ed.), pp. 91-93.2003.Springer,ISBN: 3-540-65466-6.[bib]
P. Paule, O. Scherzer, A. Schoisswohl.Wavelets with Scale Dependent Properties. In: Symbolic and Numerical Scientific Computation, F. Winkler and U. Langer (ed.), Lecture Notes in Comput. Sci.2630, pp. 255-265.2003.Springer,ISBN: 0-89871-541-5.[ps][bib]
P. Paule, H. Prodinger.Fountains, Histograms, and $q$-Identities.Discrete Math. Theor. Comput. Sci.6, pp. 101-106.2003.ISSN 1365-8050.[ps][bib]
2002
R. Lyons, P. Paule, A. Riese.A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers.Appl. Algebra Engrg. Comm. Comput.13, pp. 327-333.2002.ISSN 0938-1279.[pdf][bib]
P. Paule.Finite Actions of Groups. In: The Concise Handbook of Algebra, A.V. Mikhalev, G.F. Pilz (ed.), pp. 119-123.2002.Kluwer,ISBN 0-7923-7072-4.[bib]
I. Gutman, P. Paule.The Variance of the Vertex Degrees of Randomly Generated Graphs.Publ. Fac. Electr. Engrg. Ser. Mat.13, pp. 30-35.2002.ISSN 0354-124X.[bib]
2001
G.E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis III: The Omega Package.European J. Combin.22, pp. 887-904.2001.ISSN 0195-6698.[pdf][bib]
G.E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis VI: A New Reduction Algorithm.Ann. Comb.5, pp. 251-270.2001.ISSN 0218-0006.[pdf][bib]
G.E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis VII: Constrained Compositions. In: q-Series with Applications to Combinatorics, Number Theory, and Physics, B.C. Berndt and K. Ono (ed.), Contemp. Math.291, pp. 11-27.2001.Amer. Math. Soc.,ISBN 0-8218-2746-4.[pdf][bib]
G.E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis VIII: Plane Partition Diamonds.Adv. in Appl. Math.27, pp. 231-242.2001.ISSN 0196-8858.[pdf][bib]
G.E. Andrews, P. Paule, A. Riese.MacMahon's Partition Analysis IX: k-Gon Partitions.Bull. Austral. Math. Soc.64, pp. 321-329.2001.ISSN 0004-9727.[pdf][bib]
G.E. Andrews, P. Paule, A. Riese, V. Strehl.MacMahon's Partition Analysis V: Bijections, Recursions, and Magic Squares. In: Algebraic Combinatorics and Applications, A. Betten and others (ed.), pp. 1-39.2001.Springer,ISBN 3-5404-1110-0.[pdf][bib]
F. Chyzak, P. Paule, O. Scherzer, A. Schoisswohl, B. Zimmermann.The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval.Experiment. Math.10, pp. 67-86.2001.ISSN 1058-6458.[pdf][bib]
G.E. Andrews, A. Knopfmacher, P. Paule, B. Zimmermann.Engel Expansions of $q$-Series by Computer Algebra. In: Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F.G. Garvan and M.E.H. Ismail (ed.), Developments in Mathematics4, pp. 33-57.2001.Kluwer,ISBN: 1402001010.[pdf][bib]
G.E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger.$q$-Engel Series Expansions and Slater's Identities.Quaestiones Math.24, pp. 403-416.2001.ISSN 0379-9468.[pdf][bib]
A. Berkovich, P. Paule.Variants of the Andrews-Gordon Identities.Ramanujan J.5, pp. 391-404.2001.ISSN 1382-4090.[pdf][bib]
A. Berkovich, P. Paule.Lattice Paths, $q$-Multinomials and Two Variants of the Andrews-Gordon Identities.Ramanujan J.5, pp. 409-424.2001.ISSN 1382-4090.[pdf][bib]
2000
G.E. Andrews, A. Knopfmacher, P. Paule.An infinite family of Engel expansions of Rogers-Ramanujan type.Adv. in Appl. Math.25, pp. 2-11.2000.ISSN 0196-8858.[pdf][bib]
P. Paule.Algorithmic Problem Solving. In: Encyclopedia of Computer Science, A. Ralston, E.D. Reilly, D. Hemmendinger (ed.), pp. 38-40.2000.Nature Publishing Group, London,ISBN: 1850328005.[bib]
Peter Paule.A Mathematica Package for Extended Engel Expansions of q-series., pp. 0-0.2000.editor: K. Alladi,0.[bib]
1999
Peter Paule, Volker Strehl.Definite Summation and Hypergeometric Identities. Technical report no. 99-44 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).December1999.[ps][bib]
G.E. Andrews, P. Paule.MacMahon's Partition Analysis IV: Hypergeometric Multisums.Sém. Lothar. Combin.B42i, pp. 1-24.1999.electronic journal.[pdf][bib]
F. Chyzak, I. Gutman, P. Paule.Predicting the number of hexagonal systems with 24 and 25 hexagons.Communications in Mathematical and Computer Chemistry40, pp. 139-151.1999.ISSN: 0340-6253.[pdf][bib]
1998
S.A. Abramov, P. Paule, M. Petkovsek.$q$-Hypergeometric solutions of $q$-difference equations.Discrete Math.180, pp. 3-22.1998.ISSN 0012-365X.[pdf][bib]
1997
P. Paule, A. Riese.A Mathematica q-Analogue of Zeilberger's Algorithm Based on an Algebraically Motivated Approach to q-Hypergeometric Telescoping. In: Special Functions, q-Series and Related Topics, M.E.H. Ismail and M. Rahman (ed.), Fields Inst. Commun.14, pp. 179-210.1997.Amer. Math. Soc.,ISBN 0-8218-0524-X.[pdf][bib]
I. Nemes, P. Paule.A Canonical Form Guide to Symbolic Summation. In: Advances in the Design of Symbolic Computation Systems, A. Miola, M. Temperini (ed.), Texts Monogr. Symbol. Comput., pp. 84-110.1997.Springer, Wien-New York,ISBN 3211828443.[bib]
1996
P. Paule.A Classical Hypergeometric Proof of an Important Transformation Formula Found by J.-B. Baillon and R.E. Bruck. In: Theory and Applications of Nonlinear Operators of Accretive and Monotype Type, A. G. Kartsatos (ed.), Lecture Notes in Pure and Appl. Math.178, pp. 241-242.1996.Marcel Dekker,ISBN 0824797213.[pdf][bib]
P. Paule.A Proof of a Conjecture of Knuth.Experiment. Math.5, pp. 83-89.1996.ISSN 1058-6458.[pdf][bib]
1995
Peter Paule, Markus Schorn.A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities. Technical report no. 95-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1995.Published in Journal of Symbolic Computation..[bib]
Peter Paule, Volker Strehl.Symbolic Summation - Some Recent Developments. Technical report no. 95-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1995.Published in Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications, J. Fleischer, J. Grabmeier, F. Hehl, W. K\"uchlin (eds.), World Scientific, Singapore..[bib]
Peter Paule.Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type. Technical report no. 95-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1995.Published in The Electronic Journal of Combinatorics, vol. 1, 1994, R10.[bib]
P. Paule.Greatest Factorial Factorization and Symbolic Summation.J. Symbolic Comput.20, pp. 235-268.1995.ISSN 0747-7171.[pdf][bib]
P. Paule, M. Schorn.A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities.J. Symbolic Comput.20, pp. 673-698.1995.ISSN 0747-7171.[pdf][bib]
P. Paule, V. Strehl.Symbolic Summation - Some Recent Developments. In: Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications, J. Fleischer et al. (ed.), pp. 138-162.1995.World Scientific, Singapore,ISBN 981-02-2319-6.[pdf][bib]
1994
P. Paule.Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type.Electron. J. Combin.1, pp. 1-9.1994.ISSN 1077-8926.[pdf][bib]
1993
Petr Lisonek, Peter Paule, Volker Strehl.Improvement of the Degree Setting in Gosper's Algorithm. Technical report no. 93-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).January1993.[bib]
Peter Paule.Greatest-Factorial Factorization and Symbolic Summation I. Technical report no. 93-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1993.Published in: · Journal Journal of Symbolic Computation archive Volume 20 Issue 3, Sept. 1995 Pages 235 - 268 ..[bib]
Peter Paule, Markus Schorn.A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities - A Description How to Use It. Technical report no. 93-36 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1993.Published in: Journal of Symbolic Computation Volume 20, Issues 5–6, November 1995, Pages 673-698..[bib]
G. E. Andrews, P. Paule.Some Questions Concerning Computer-Generated Proofs of a Binomial Double-Sum Identity.J. Symbolic Comput.16, pp. 147-153.1993.ISSN 0747-7171.[pdf][bib]
R. Folk, A. Kartashov, P. Lisonek, P. Paule.Symmetries in Neural Networks: A Linear Group Approach.J. Phys. A26, pp. 3159-3164.1993.ISSN 0305-4470.[bib]
P. Lisonek, P. Paule, V. Strehl.Improvement of the Degree Setting in Gosper's Algorithm.J. Symbolic Comput.16, pp. 243-258.1993.ISSN 0747-7171.[pdf][bib]
1992
Peter Paule.Solution of a Seminaire Homework Example ($28^th$ SLC). Technical report no. 92-59 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1992.Published in Talk presented at the 28th Seminaire Lotharingien de Combinatoire, March 15-18, 1992, Domaine Saint-Jaques, France. Paper to be submitted for publication..[bib]
1991
Peter Paule, Volker Strehl.A Remark on an Instance of Gosper's Algorithm. Technical report no. 91-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1991.[bib]
George E. Andrews, Peter Paule.Some Questions Concerning Computer-Generated Proofs of Double-Sum Identity. Technical report no. 91-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1991.Published in: Journal of Symbolic Computation Volume 16, Issue 2, August 1993, Pages 147-151..[bib]
1990
Peter Paule.Computer Algebra Algorithmen f{\"u}r q-Reihen und kombinatorische Identit{\"a}ten. Technical report no. 90-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1990.[bib]
Peter Paule.Solution to Amer. Math. Monthly Problem E3376. Technical report no. 90-48 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1990.[bib]
Peter Paule.Parallel Algorithms in Computer Algebra Zeilberger's Holonomic Systems Approach. Technical report no. 90-49 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1990.[bib]
Peter Paule.Mathematica Overview. Technical report no. 90-62 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1990.Published in J. of Automated Reasoning..[bib]
Peter Paule.An Algorithmic Construction of Combinatorial Bijections as an Application of a Lemma of Ingleton and Piff. Technical report no. 90-66 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1990.[bib]
1989
P. PAULE.A Lagrange Inversion Proof of a Conjecture of J.D. Louck. Technical report no. 89-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1989.[bib]
P. PAULE.Mellin's Series from One Variable Lagrange-Inversion. Technical report no. 89-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1989.[bib]
1988
P. PAULE. Mathematik f\"ur Informatiker III (WS 1987/88). Technical report no. 88-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online).1988.[bib]
1987
P. Paule.A Note on Bailey's Lemma.J. Combin. Theory Ser. A44, pp. 164-167.1987.ISSN 0097-3165.[pdf][bib]
P. Paule.A Remark on a Lemma of Ingleton and Piff and the Construction of Bijections.Bayreuth. Math. Schr.25, pp. 123-127.1987.ISSN 0172-1062.[pdf][bib]
P. Paule.The Concept of Bailey Chains.Sém. Lothar. Combin.B18f, pp. 1-24.1987.electronic journal.[pdf][bib]
1986
P. Paule.Über das Involutionsprinzip von Garsia und Milne.Bayreuth. Math. Schr.21, pp. 295-319.1986.ISSN 0172-1062.[pdf][bib]
1985
P. Paule.On Identities of the Rogers-Ramanujan Type.J. Math. Anal. Appl.107, pp. 255-284.1985.ISSN 0022-247X.[bib]
P. Paule.Ein neuer Weg zur q-Lagrangeinversion.Bayreuth. Math. Schr.18, pp. 1-37.1985.ISSN 0172-1062.[pdf][bib]
P. Paule.Über die Inversionsstatistiken von MacMahon und Goulden-Jackson.Sém. Lothar. Combin.B13b, pp. 1-3.1985.electronic journal.[pdf][bib]
1982
Peter Paule.Zwei neue Transformationen als elementare Anwendungen der q-Vandermonde Formel. University of Vienna. PhD Thesis.1982.[bib]