Symbolic Summation
Hypergeometric Summation

fastZeil,
the Paule/Schorn implementation of Gosper's and Zeilberger's
algorithm in Mathematica (by P. Paule, M. Schorn, and A. Riese).

Zeilberger,
a Maxima implementation of Gosper's and Zeilberger's
algorithm (by F. Caruso).

MultiSum,
a Mathematica package for proving hypergeometric multisum
identities (by K. Wegschaider and A. Riese).
qHypergeometric Summation

qZeil,
a Mathematica implementation of qanalogues of Gosper's
and Zeilberger's algorithm (by A. Riese).

Bibasic Telescope (pqTelescope),
a Mathematica implementation of a generalization of
Gosper's algorithm to bibasic hypergeometric summation (by A. Riese).

qMultiSum,
a Mathematica package for proving qhypergeometric
multisum identities (by A. Riese).
MultiSummation in Difference Rings and Fields

Sigma,
a Mathematica package for discovering and proving multisum identities (by C. Schneider).
Symbolic Summation for Stirling Numbers

Stirling,
a Mathematica package for computing recurrence equations of sums
involving Stirling numbers or Eulerian numbers (by M. Kauers).
Symbolic Summation and Integration for Holonomic Functions

HolonomicFunctions,
a Mathematica package for dealing with multivariate holonomic functions,
including closure properties, summation, and integration (by C. Koutschan).
Sequences and Power Series

Asymptotics,
a Mathematica package for computing asymptotic series expansions of univariate
holonomic sequences (by M. Kauers).

Dependencies,
a Mathematica package for computing algebraic relations of Cfinite sequences
and multisequences (by M. Kauers and B. Zimmermann).

Engel,
a Mathematica implementation of qEngel Expansion
(by B. Zimmermann).

GeneratingFunctions,
a Mathematica package for manipulations of
univariate holonomic functions and sequences (by C. Mallinger).

ore_algebra,
a Sage package for doing computations with Ore operators (by M. Kauers, M. Jaroschek, F Johansson).

qGeneratingFunctions,
a Mathematica package for manipulations of
univariate qholonomic functions and sequences (by C. Koutschan).

Guess,
a Mathematica package for guessing multivariate recurrence equations (by M. Kauers).

RLangGFun,
a Maple implementation of the inverse Schützenberger methodology
(by C. Koutschan).
Special Function Algorithms for Indefinite Nested Sums and Integrals

HarmonicSums,
a Mathematica package for dealing with harmonic sums, generalized harmonic sums and
cyclotomic sums and their related integral representations (by J. Ablinger).
Permutation Groups

PermGroup,
a Mathematica package for permutation groups, group actions
and Polya theory (by T. Bayer).
Partition Analysis

Omega,
a Mathematica implementation of Partition Analysis (by A. Riese).

GenOmega,
a Mathematica implementation of GuoNiu Han's general Algorithm for
MacMahon's Partition Analysis (by M. Wiesinger).
Difference/Differential Equations

DiffTools,
a Mathematica implementation of several algorithms for
solving linear difference equations with polynomial coefficients (by C. Weixlbaumer).

OreSys,
a Mathematica implementation of several algorithms for
uncoupling systems of linear Ore operator equations (by S. Gerhold).

RatDiff,
a Mathematica implementation of Mark van Hoeij's algorithm for
finding rational solutions of linear difference equations (by A. Riese).

SumCracker,
a Mathematica implementation of several algorithms for
identities and inequalities of special sequences, including
summation problems (by M. Kauers).
Misc

Singular,
a Mathematica interface to the Singular system
(by M. Kauers and V. Levandovskyy).

ModularGroup, a
Mathematica package providing basic algorithms and visualization
routines related to the modular group, e.g. for drawing the
tessellation of the upper halfplane (by T. Ponweiser).
