sumtools - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Discrete Mathematics : Summation and Difference Equations : SumTools : sumtools/sumrecursion

sumtools

  

sumrecursion

  

Zeilberger's algorithm

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

sumrecursion(f, k, s(n))

Parameters

f

-

expression

k

-

name, summation variable

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

kfk

  

the sum to be taken over all integers k, with respect to n if f is an (m,l)-fold hypergeometric term with respect to (n,k) for some m and l. The minimal values for m, and l are determined automatically.

• 

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

• 

An expression f is called (m,l)-fold hypergeometric term with respect to (n,k) if

fsubsn=nm,fandfsubsk=kl,f

  

are rational with respect to n and k. This is typically the case for ratios of products of rational functions, exponentials, factorials, binomial coefficients, and Pochhammer symbols that are rational-linear in their arguments. The implementation supports this type of input.

• 

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

Examples

withsumtools

Hypersum,Sumtohyper,extended_gosper,gosper,hyperrecursion,hypersum,hyperterm,simpcomb,sumrecursion,sumtohyper

(1)

sumrecursionbinomialn,k3,k,fn

8n12fn27n27n+2fn1+fnn2

(2)

sumrecursionbinomialn,k2binomial2k,n,k,sn

8n12sn27n27n+2sn1+snn2

(3)

Dougall's identity

fhyperterma,1+a2,b,c,d,1+2abcd+n,n,a2,1+ab,1+ac,1+ad,1+a1+2abcd+n,1+a+n,1,khyperterm1+a,1+abc,1+abd,1+acd,1,1+ab,1+ac,1+ad,1+abcd,1,n

f:=pochhammera,kpochhammer1+12a,kpochhammerb,kpochhammerc,kpochhammerd,kpochhammer1+2abcd+n,kpochhammern,kpochhammer1+ab,npochhammer1+ac,npochhammer1+ad,npochhammer1+abcd,npochhammer12a,kpochhammer1+ab,kpochhammer1+ac,kpochhammer1+ad,kpochhammera+b+c+dn,kpochhammer1+a+n,kk!pochhammer1+a,npochhammer1+abc,npochhammer1+abd,npochhammer1+acd,n

(4)

sumrecursionf,k,sn

snsn1

(5)

See Also

sum

sumtools

sumtools[gosper]

SumTools[Hypergeometric][Zeilberger]

sumtools[hyperterm]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam