q-Hypergeometric solutions of q-difference equations

Abstract We present algorithm qHyper for finding all solutions y ( x ) of a linear homogeneous q -difference equation, such that y ( qx )= r ( x ) y ( x ) where r ( x ) is a rational function of x . Applications include construction of basic hypergeometric series solutions, and definite q -hypergeometric summation in closed form.

[1]  Manuel Bronstein,et al.  An Introduction to Pseudo-Linear Algebra , 1996, Theor. Comput. Sci..

[2]  Marko Petkovsek,et al.  Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficents , 1992, J. Symb. Comput..

[3]  Doron Zeilberger,et al.  Rational functions certify combinatorial identities , 1990 .

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

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

[6]  Peter Paule,et al.  Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type , 1994, Electron. J. Comb..

[7]  Richard P. Stanley,et al.  Differentiably Finite Power Series , 1980, Eur. J. Comb..

[8]  Sergei A. Abramov.  Rational solutions of linear difference and q-difference equations with polynomial coefficients , 1995, ISSAC '95.

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

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

[11]  Peter Paule,et al.  SYMBOLIC SUMMATION SOME RECENT DEVELOPMENTS , 1995 .

[12]  Peter Paule,et al.  A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities , 1995, J. Symb. Comput..

[13]  Manuel Bronstein,et al.  On polynomial solutions of linear operator equations , 1995, ISSAC '95.

[14]  Emil Grosswald,et al.  The Theory of Partitions , 1984 .

[15]  Manuel Bronstein,et al.  On ore rings, linear operators and factorisation , 1993 .

[16]  Diploma Thesis,et al.  A Mathematica q-Analogue of Zeilberger's Algorithm for Proving q-Hypergeometric Identities , 1995 .