SumTools[DefiniteSum] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Discrete Mathematics : Summation and Difference Equations : SumTools : DefiniteSum Subpackage : SumTools/DefiniteSum/CreativeTelescoping

SumTools[DefiniteSum]

  

CreativeTelescoping

  

compute closed forms of definite sums using creative telescoping method

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

CreativeTelescoping(f, k=m..n)

Parameters

f

-

hypergeometric term

k

-

name; summation index

m, n

-

expressions or integers

Description

• 

The CreativeTelescoping(f, k=m..n) command computes a closed form of the definite sum of f over the specified range of k using creative telescoping method.

Examples

withSumToolsDefiniteSum:

Fbinomial2n,2k2

F2n2k2

(1)

k=0nF=CreativeTelescopingF,k=0..n

k=0n2n2k2=−1n2nn2+4n2n2

(2)

References

  

van Hoeij, M. "Finite Singularities and Hypergeometric Solutions of Linear Recurrence Equations." Journal of Pure and Applied Algebra. Vol. 139. (1999): 109-131.

  

Zeilberger, D. "The Method of Creative Telescoping." Journal of Symbolic Computing. Vol. 11. (1991): 195-204.

See Also

SumTools[DefiniteSum]

SumTools[DefiniteSummation]

SumTools[Hypergeometric]

SumTools[Summation]