SumTools[Hypergeometric]
ExtendedGosper
perform extended Gosper's algorithm
Calling Sequence
Parameters
Description
Examples
References
ExtendedGosper(T, n)
T
-
list or set of hypergeometric terms of n
n
variable
Let En be the shift operator with respect to n, defined by Enfn=fn+1. For the given set (list)
T={t1n,...,tpn}
where the tin are hypergeometric terms of n, the ExtendedGosper(T,n) command returns a set (list)
S={s1n,...,sqn}
of hypergeometric terms sin such that
En−1∑i=1qsin=∑j=1ptjn
if each of the hypergeometric term sin exists. Otherwise, the ExtendedGosper routine returns the error message ``no solution found''.
withSumToolsHypergeometric:
T≔−1kbinomialn,kkj,n2an,−n2an+n+12an+1
T≔n2an,−1knkkj,−n2an+n+12an+1
ExtendedGosperT,n
a2n2−2an2−2an+n2+a+2n+1an+1a3−3a2+3a−1,−−n+k−1knkkjk+1
T≔n24nn+1n+2,22n−1n2n+1binomial2n,n,−n24nn+1n+2+n+124n+1n+2n+3
T≔n24nn+1n+2,22n−1n2n+12nn,−n24nn+1n+2+n+124n+1n+2n+3
−22n−12nnn,n−14n+13n+2
No solution found:
T≔2n+1n2−3n2an,n2an
T≔n2an,2n+1n2ann2−3
Error, (in SumTools:-Hypergeometric:-ExtendedGosper) no solution found
Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.
See Also
sumtools/extended_gosper
SumTools[Hypergeometric][Gosper]
Download Help Document