SumTools[Hypergeometric]
KoepfGosper
indefinite summation of j-fold hypergeometric terms
Calling Sequence
Parameters
Description
Examples
References
KoepfGosper(T, n)
T
-
hypergeometric term in n
n
name; specifies summation index
The KoepfGosper(T, n) command solves the problem of indefinite summation of j-fold hypergeometric terms, that is, for the input j-fold hypergeometric term T of n, it constructs a function which is a sum of hypergeometric terms of n such that , provided that such a exists. Otherwise, the function returns the error message ``no solution found''.
The parameter T is a j-fold hypergeometric term in n if is a rational function in n.
Note that T is not a hypergeometric term in n. Hence, Gosper's algorithm is not applicable to T.
Koepf, W. "Algorithms for m-fold Hypergeometric Summation." Journal of Symbolic Computation. Vol. 20 No. 4. (1995): 399-417.
Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, 1998.
See Also
SumTools[Hypergeometric][Gosper]
SumTools[Hypergeometric][KoepfZeilberger]
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