Zeilberger-Koepf's hyperrecursion algorithm - Maple Help

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sumtools[hyperrecursion] - Zeilberger-Koepf's hyperrecursion algorithm

Calling Sequence

hyperrecursion(U, L, z, s(n))

Parameters

U, L

-

lists of the upper and lower parameters

z

-

evaluation point

n

-

name, recurrence variable

s

-

name, recurrence function

Description

• 

This function is an implementation of Koepf's extension of Zeilberger's algorithm, calculating a (downward) recurrence equation for the sum

khypertermU,L,k

  

the sum to be taken over all integers k, with respect to n. Here, U and L denote the lists of upper and lower parameters, and z is the evaluation point. The arguments of U and L are assumed to be rational-linear with respect to n. The resulting expression equals zero.

• 

The output is a recurrence which equals zero. The recurrence is output as a function of n, the recurrence variable, and sn,sn1,....

• 

The command with(sumtools,hyperrecursion) allows the use of the abbreviated form of this command.

Examples

withsumtools:

hyperrecursionn,a,b,1,fn

n+ab+1fn1+b+n1fn

(1)

Dougall's identity

hyperrecursiona,1+a2,b,c,d,1+2abcd+n,n,a2,1+ab,1+ac,1+ad,1+a1+2abcd+n,1+a+n,1,sn

a+nacd+nabd+nabc+nsn1+snad+nac+nab+nabcd+n

(2)

hyperrecursiona+12,a,b,1b,n,2a+13+n,a2+1,12,2ab+33,2a+b+23,3n,2a+1+3n,a2,1,sn

b2+3nb+13n2a1+3n2a+3nsn1+sn3n13n23nb+2a1+3n+b+2a

(3)

See Also

sum, sumtools, sumtools[gosper], SumTools[Hypergeometric][Zeilberger], sumtools[hypersum], sumtools[hyperterm], sumtools[sumrecursion]


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