indefinite summation of j-fold hypergeometric terms
hypergeometric term in 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 G which is a sum of hypergeometric terms of n such that T⁡n=G⁡n+1−G⁡n, provided that such a G exists. Otherwise, the function returns the error message ``no solution found''.
The parameter T is a j-fold hypergeometric term in n if T⁡n+jT⁡n is a rational function in n.
T ≔ n⁢n2!
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.
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