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, 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]
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 (ed.), Tetsuo Ida.An Introduction to Computational Origami.Texts and Monographs of Symbolic Computation1st edition,2020.Springer,978-3-319-59189-6.[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 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]
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]
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.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.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
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, 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
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
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
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]
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]
