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pochhammer

general pochhammer function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

pochhammer(z, a)

Parameters

z

-

expression

a

-

expression

Description

• 

The pochhammer symbol is defined for a positive integer n and complex number z as

pochhammerz,n=zz+1...z+n1

  

This is extended analytically to complex n by using the formula

  

 

pochhammerz,a=Γz+aΓz

• 

At all points z,a such that z and z+a are positive integers, this is equivalent to:

pochhammerz,a=limt0Γz+a+tΓz+t

  

In the case that z is a non-positive integer, pochhammer(z,a) is defined by this limit.

  

In the case that both z and z+a are non-positive integers, Maple also signals the invalid_operation numeric event, allowing the user to control this singular behavior by catching the event. See numeric_events for more information.

Examples

pochhammer5,3

210

(1)

pochhammerz,2

pochhammerz,2

(2)

pochhammerz,3

1pochhammer3+z,3

(3)

pochhammer2,I

Γ2+I

(4)

NumericStatusinvalid_operation=false:

pochhammer3,2

6

(5)

NumericStatusinvalid_operation=false

invalid_operation=true

(6)

pochhammer0,0

1

(7)

NumericStatusinvalid_operation

true

(8)

xpochhammera,x

pochhammera,xΨx+a

(9)

apochhammera,x

pochhammera,xΨx+aΨa

(10)

seriespochhammera,x,x,3

1+Ψax+Ψ1,a2+Ψa22x2+Ox3

(11)

pochhammerx,5

pochhammerx,5

(12)

expand

x5+10x4+35x3+50x2+24x

(13)

pochhammer2,13

8π327Γ23

(14)

evalf

1.190639350

(15)

pochhammer3.7+2.2I,1.5+2.7I

−0.0005620896042+0.01961129135I

(16)

convertpochhammera,x,GAMMA

Γx+aΓa

(17)

convertpochhammera,x,binomial

a+x1a1x!

(18)

convertpochhammera,x,factorial

a+x1!a1!

(19)

See Also

convert

diff

evalf

expand

GAMMA

initialfunctions

NumericStatus

series