JacobiZeta
Jacobi's Zeta function
Calling Sequence
Parameters
Description
Examples
JacobiZeta(z, k)
z
-
algebraic expression
k
JacobiZeta is defined by:
FunctionAdvisor(definition, JacobiZeta);
JacobiZetaz,k=ⅆⅆzlnJacobiTheta4πz2EllipticKk,EllipticNomek,with no restrictions on z,k
which is essentially the logarithmic derivative of JacobiTheta4.
JacobiZeta(z,k) is a periodic function of z with period 2EllipticKk
JacobiZeta1.0,0.5
0.06347769531
FunctionAdvisorspecial_values,JacobiZeta
JacobiZeta−z,k=−JacobiZetaz,k,JacobiZetaz,−k=JacobiZetaz,k,JacobiZeta0,k=0,JacobiZetaz,0=0,JacobiZetaz,1=tanhz,JacobiZetaz,∞=∞+∞I,JacobiZeta2_n1EllipticKk,k=0,_n1::ℤ
FunctionAdvisorsum_form,JacobiZeta
JacobiZetaz,k=∑_k1=1∞−2πEllipticNomek_k1sin_k1πzEllipticKkEllipticKkEllipticNomek2_k1−1,with no restrictions on z,k
See Also
EllipticE
EllipticK
EllipticNome
FunctionAdvisor
JacobiTheta4
Zeta
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