product representations of Jacobi ϑ functions


The Jacobi theta functionsMathworldPlanetmath can be expressed as infinite products:

ϑ1(z;q)=2q1/4sinzn=1(1-q2n)(1-2q2ncos2z+q4n)
ϑ2(z;q)=2q1/4coszn=1(1-q2n)(1+2q2ncos2z+q4n)
ϑ3(z;q)=n=1(1-q2n)(1+2q2n-1cos2z+q4n-2)
ϑ4(z;q)=n=1(1-q2n)(1-2q2n-1cos2z+q4n-2)
Title product representations of Jacobi ϑ functionsMathworldPlanetmath
Canonical name ProductRepresentationsOfJacobivarthetaFunctions
Date of creation 2013-03-22 14:52:13
Last modified on 2013-03-22 14:52:13
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 4
Author rspuzio (6075)
Entry type Theorem
Classification msc 33E05