Zeilberger-Koepf's hypersum algorithm - Maple Help

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

sumtools[Hypersum] - Zeilberger-Koepf's algorithm

Calling Sequence

hypersum(U, L, z, n)

Hypersum(U, L, z, n)

Parameters

U, L

-

lists of the upper and lower parameters

z

-

evaluation point

n

-

name, recurrence variable

Description

• 

This function is an implementation of Zeilberger-Koepf's algorithm, and calculates a closed form for the sum

khypertermU,L,k

  

the sum to be taken over all integers k, with respect to n, whenever an extension of Zeilberger's algorithm gives a suitable recurrence equation. 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 procedure Hypersum is the corresponding inert form which remains unevaluated.

• 

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

Examples

withsumtools:

Dougall's identity

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

pochhammer1+a,npochhammerabc+1,npochhammerabd+1,npochhammeracd+1,npochhammer1+ab,npochhammer1+ac,npochhammer1+ad,npochhammerabcd+1,n

(1)

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

Hyperterm1,1+a,abc+1,abd+1,acd+1,1+ab,1+ac,1+ad,abcd+1,1,n

(2)

Andrews

Hypersumn,n+3a,a,3a2,3a+12,34,n

{Hyperterm1,23,13,23+a,a+13,1,13niremn,3=00iremn,3=10iremn,3=2

(3)

See Also

sum, sumtools, SumTools[Hypergeometric][KoepfZeilberger]


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