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sumtools

  

sumtohyper

  

express an indefinite sum as a Hypergeometric function

  

Sumtohyper

  

express an indefinite sum as a Hypergeometric function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

sumtohyper(f, k)

Sumtohyper(f, k)

Parameters

f

-

expression

k

-

name, summation variable

Description

• 

The function sumtohyper converts the sum

kfk

  

to be taken over all integers k, involving exponentials, factorials, binomial coefficients, and Pochhammer symbols into hypergeometric notation. The procedure Sumtohyper is the corresponding inert form which gives the result in terms of an unevaluated Hypergeom expression.

• 

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

Examples

withsumtools:

sumtohyperbinomialn,k,k

2n

(1)

Sumtohyperbinomialn,k,k

Hypergeomn,,1

(2)

sumtohyperbinomialn,k2,k

Γ1+2nΓn+12

(3)

sumtohyperbinomialn,k2binomialn1,k2,k

3n2Γ2n1Γn2n

(4)

See Also

hypergeom

sum

sumtools

 


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