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combine/Psi

combine Psi functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

combine(f, Psi)

combinef,Ψ

Parameters

f

-

any expression

Description

• 

Expressions involving Psi are combined as follows

Ψn±x+Ψm±xΨx±Qx±πPcotπx

  

where Q is a rational function, P a univariate polynomial and m and n are rationals.

• 

This is done by applying the following recurrence and reflection formulae.

Ψ1+x=Ψx+1x

Ψ1x=Ψx+πcotπx

Ψn,1+x=Ψn,x+−1nn!xn+1

Ψn,1x=−1nΨn,x+ⅆnⅆxnπcotπx

• 

You can enter the command combine/Psi using either the 1-D or 2-D calling sequence. For example, combine(Psi(x) + Psi(1+x), Psi) is equivalent to combineΨx+Ψ1+x,Ψ.

Examples

combineΨx+Ψ1+x,Ψ

2Ψx+1x

(1)

combineΨ1xΨx+Ψy,Ψ

πcotπx+Ψy

(2)

combineΨ2,x12Ψ2,x+12,Ψ

2x123

(3)

combineΨ1,x12Ψ1,x+12,Ψ

1x122

(4)

See Also

combine

GAMMA

Psi

 


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