integral represetations of Jacobi ϑ functions
The Jacobi theta functions have the following integral representations:
ϑ1(z|τ)=-eiz+iπτ/4∫i+∞i-∞eiπτu2cos(2uz+πτu)sin(πu)du |
ϑ2(z|τ)=-ieiz+iπτ/4∫i+∞i-∞eiπτu2cos(2uz+πu+πτu)sin(πu)du |
ϑ3(z|τ)=-i∫i+∞i-∞eiπτu2cos(2uz+πu)sin(πu)du |
ϑ4(z|τ)=-i∫i+∞i-∞eiπτu2cos(2uz)sin(πu)du |
Title | integral represetations of Jacobi ϑ functions![]() |
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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 |