integral represetations of Jacobi ϑ functions


The Jacobi theta functionsMathworldPlanetmath have the following integral representations:

ϑ1(z|τ)=-eiz+iπτ/4i-i+eiπτu2cos(2uz+πτu)sin(πu)du
ϑ2(z|τ)=-ieiz+iπτ/4i-i+eiπτu2cos(2uz+πu+πτu)sin(πu)du
ϑ3(z|τ)=-ii-i+eiπτu2cos(2uz+πu)sin(πu)du
ϑ4(z|τ)=-ii-i+eiπτu2cos(2uz)sin(πu)du
Title integral represetations of Jacobi ϑ functionsMathworldPlanetmath
Canonical name IntegralRepresetationsOfJacobivarthetaFunctions
Date of creation 2013-03-22 14:39:52
Last modified on 2013-03-22 14:39:52
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 12
Author rspuzio (6075)
Entry type Theorem
Classification msc 33E05