Handling Hypergeometric Series in Maple
نویسندگان
چکیده
This paper discusses and evaluates the standard procedures available in Maple 4.3 for handling hypergeometric series. Some suggestions for improvement are given. The paper concludes with a survey of the algorithms of Gosper and of Zeilberger for possibly evaluating a terminating series of hypergeometric type. This paper appeared in Orthogonal polynomials and their applications, C. Brezinski, L. Gori and A. Ronveaux (eds.), IMACS Annals on Computing and Applied Mathematics 9, Baltzer, 1991, pp. 73–80. The text of the present version (October 19, 2006) is unchanged except that references have been updated.
منابع مشابه
An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients
In 1992, Koepf [J. Symb. Comp. 13 (1992) 581] introduced an algorithm for computing a Formal Power Series of a given function using generalized hypergeometric series and a recurrence equation of hypergeometric type. The main aim of this paper is to develop a new algorithm for computing exact power series solutions of second order linear differential equations with polynomial coefficients, near ...
متن کاملAlgorithmic determination of q-power series for q-holonomic functions
In [Koepf (1992)] it was shown how for a given holonomic function a representation as a formal power series of hypergeometric type can be determined algorithmically. This algorithm – that we call FPS algorithm (Formal Power Series) – combines three steps to obtain the desired representation. The authors implemented this algorithm in the computer algebra system Maple as c̀onvert/FormalPowerSeries...
متن کاملOn Zeilberger’s algorithm and its q-analogue: a rigorous description
Gosper’s and Zeilberger’s algorithms for summation of terminating hypergeometric series as well as the q-versions of these algorithms are described in a very rigorous way. The paper is a companion to Maple V procedures implementing these algorithms. It concludes with the help information for these procedures.
متن کاملFinding Identities with the WZ Method
Extending the work of Wilf and Zeilberger on WZ-pairs, we describe how new terminating hypergeometric series identities can be derived by duality from known identities. A large number of such identities are obtained by a Maple program that applies this method systematically.
متن کاملAsymptotic Approximations to Truncation Errors of Series Representations for Special Functions
∞ ν=0 aν for special functions are constructed by solving a system of linear equations. The linear equations follow from an approximative solution of the inhomogeneous difference equation ∆rn = an+1. In the case of the remainder of the Dirichlet series for the Riemann zeta function, the linear equations can be solved in closed form, reproducing the corresponding Euler-Maclaurin formula. In the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1991