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SumTools[Hypergeometric]

  

KoepfGosper

  

indefinite summation of j-fold hypergeometric terms

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

KoepfGosper(T, n)

Parameters

T

-

hypergeometric term in n

n

-

name; specifies summation index

Description

• 

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 Tn=Gn+1Gn, 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 Tn+jTn is a rational function in n.

Examples

withSumToolsHypergeometric:

Tnn2!

Tnn2!

(1)

KoepfGosperT,n

2n2!+2n2+12!

(2)

IsHypergeometricTermT,n

false

(3)

Note that T is not a hypergeometric term in n. Hence, Gosper's algorithm is not applicable to T.

References

  

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]

SumTools[Hypergeometric][Gosper]

SumTools[Hypergeometric][KoepfZeilberger]