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SumTools[Hypergeometric]

  

ExtendedGosper

  

perform extended Gosper's algorithm

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

ExtendedGosper(T, n)

Parameters

T

-

list or set of hypergeometric terms of n

n

-

variable

Description

• 

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 t[i]n are hypergeometric terms of n, the ExtendedGosper(T,n) command returns a set (list)

S={s1n,...,sqn}

  

of hypergeometric terms s[i]n such that

En1i=1qsin=j=1ptjn

  

if each of the hypergeometric term s[i]n exists. Otherwise, the ExtendedGosper routine returns the error message ``no solution found''.

Examples

withSumTools[Hypergeometric]:

T1kbinomialn,kkj,n2an,n2an+n+12an+1

T:=n2an,1kbinomialn,kkj,n2an+n+12an+1

(1)

ExtendedGosperT,n

a2n22an22an+n2+a+2n+1an+1a33a2+3a1,n+k1kbinomialn,kkjk+1

(2)

Tn24nn+1n+2,22n1n2n+1binomial2n,n,n24nn+1n+2+n+124n+1n+2n+3

T:=n24nn+1n+2,22n1n2n+1binomial2n,n,n24nn+1n+2+n+124n+1n+2n+3

(3)

ExtendedGosperT,n

22n1binomial2n,nn,13n14n+1n+2

(4)

No solution found:

Tn2an,2n+1n2ann23

T:=n2an,2n+1n2ann23

(5)

ExtendedGosperT,n

Error, (in SumTools:-Hypergeometric:-ExtendedGosper) no solution found

References

  

Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.

See Also

sumtools/extended_gosper

SumTools[Hypergeometric]

SumTools[Hypergeometric][Gosper]

 


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