perform extended Gosper's algorithm
list or set of hypergeometric terms of n
Let En be the shift operator with respect to n, defined by En⁡f⁡n=f⁡n+1. For the given set (list)
where the ti⁡n are hypergeometric terms of n, the ExtendedGosper(T,n) command returns a set (list)
of hypergeometric terms si⁡n such that
if each of the hypergeometric term si⁡n exists. Otherwise, the ExtendedGosper routine returns the error message ``no solution found''.
T ≔ −1k⁢binomial⁡n,k⁢kj,n2⁢an,−n2⁢an+n+12⁢an+1
T ≔ n2⁢4nn+1⁢n+2,22⁢n−1n⁢2⁢n+1⁢binomial⁡2⁢n,n,−n2⁢4nn+1⁢n+2+n+12⁢4n+1n+2⁢n+3
No solution found:
T ≔ n2⁢an,2⁢n+1⁢n2⁢ann2−3
Error, (in SumTools:-Hypergeometric:-ExtendedGosper) no solution found
Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.
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