In 1978, W. Gosper gave an algorithm to compute the indefinite sum of an hypergeometric sequence. This algorithm has been incorporated in most computer algebra systems as the basis of their summation routines. Then, in the early 1990's D. Zeilberger applied a version of Gosper's algorithm in a clever way to the efficient calculation of definite sums of hypergeometric sequences. Zeilberger also gave a very general but slow algorithm for the general case of holonomic functions. F. Chyzak shows how Zeilberger's fast algorithm can be extended to a much more general context, including summation and integration of holonomic functions and sequences.










=(1)^{n}p I_{n}(p),  








n 
k 
Ci  (z)=  ó õ 


. 

t_{n}, 
P· 

t_{n}=[Q· t_{n}]_{a}^{b}. 
ì í î 

P=D_{z}, Q= 

+ 

D_{z}, 
D_{z}· 

J_{k}(z)^{2}+[Q·  J_{k}(z)^{2}] 

=0. 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.