MultInt, a MAPLE Package for Multiple Integration by the WZ Method

We describe a MAPLE implementation, MultInt, of the continuous version of the WZ method. We also give various examples of how this package can be used to systematically generate proofs of identities (or recurrences) which involve multiple integrals of proper-hyperexponential functions. Moreover, by expressing a binomial coefficient sum as a hyperexponential contour or multi-contour integral, the package provides an alternative approach to sums.

[1]  Volker Strehl,et al.  Binomial identities - combinatorial and algorithmic aspects , 1994, Discret. Math..

[2]  George E. Andrews,et al.  q-series : their development and application in analysis, number theory, combinatorics, physics, and computer algebra , 1986 .

[3]  Axel. Riese,et al.  FINE-TUNING ZEILBERGER ’ S ALGORITHM The Methods of Automatic Filtering and Creative Substituting , 2002 .

[4]  Wolfram Koepf,et al.  Algorithms for q-Hypergeometric Summation in Computer Algebra , 1999, J. Symb. Comput..

[5]  Peter Paule,et al.  A Mathematica q-Analogue of Zeilberger's Algorithm Based on an Algebraically Motivated Approach to q-Hypergeometric Telescoping , 1991 .

[6]  Shalosh B. Ekhad,et al.  A one-line proof of the Habsieger-Zeilberger G2 constant term identity☆ , 1991 .

[7]  Doron Zeilberger,et al.  A proof of the G 2 case of macdonald's root system-dyson conjecture , 1987 .

[8]  G. Egorychev.  Integral representation and the computation of combinatorial sums , 1984 .

[9]  I. J. Good,et al.  Short Proof of a Conjecture by Dyson , 1970 .

[10]  George E. Andrews,et al.  Some Questions Concerning Computer-Generated Proofs of a Binomial Double- Sum Identy , 1993, J. Symb. Comput..

[11]  Frédéric Chyzak.  Gröbner Bases and Applications: Gröbner Bases, Symbolic Summation and Symbolic Integration , 1998 .

[12]  Doron Zeilberger,et al.  An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities , 1992 .

[13]  Mourad E. H. Ismail,et al.  Special functions, q-series, and related topics , 1997 .

[14]  I. G. MacDonald,et al.  Some Conjectures for Root Systems , 1982 .

[15]  Tom H. Koornwinder,et al.  On Zeilberger's algorithm and its q-analogue: a rigorous description , 1993 .

[16]  Doron Zeilberger,et al.  A fast algorithm for proving terminating hypergeometric identities , 1990, Discret. Math..

[17]  B. Berndt,et al.  q‐SERIES: THEIR DEVELOPMENT AND APPLICATION IN ANALYSIS, NUMBER THEORY, COMBINATORICS, PHYSICS, AND COMPUTER ALGEBRA (CBMS Regional Conference Series in Mathematics 66) , 1987 .

[18]  Akalu Tefera.  A Multiple Integral Evaluation Inspired by the Multi-WZ Method , 1999, Electron. J. Comb..