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JacobiZeta

Jacobi's Zeta function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

JacobiZeta(z, k)

Parameters

z

-

algebraic expression

k

-

algebraic expression

Description

• 

JacobiZeta is defined by:

FunctionAdvisor(definition, JacobiZeta);

JacobiZetaz,k=DifflnJacobiTheta412πzEllipticKk,EllipticNomek,z,with no restrictions on z,k

(1)
  

which is essentially the logarithmic derivative of JacobiTheta4.

• 

JacobiZeta(z,k) is a periodic function of z with period 2EllipticKk

Examples

JacobiZeta1.0,0.5

0.06347769531

(2)

FunctionAdvisorspecial_values,JacobiZeta

JacobiZetaz,k=JacobiZetaz,k,JacobiZetaz,k=JacobiZetaz,k,JacobiZeta0,k=0,JacobiZetaz,0=0,JacobiZetaz,1=tanhz,JacobiZetaz,=+I,JacobiZeta2_n1EllipticKk,k=0,_n1::'integer'

(3)

FunctionAdvisorsum_form,JacobiZeta

JacobiZetaz,k=_k1=12πEllipticNomek_k1sin_k1πzEllipticKkEllipticKkEllipticNomek2_k11,with no restrictions on z,k

(4)

See Also

EllipticE

EllipticK

EllipticNome

FunctionAdvisor

JacobiTheta4

Zeta