The Jacobi theta functions JacobiTheta1, JacobiTheta2, JacobiTheta3, JacobiTheta4 are defined by:

These series converge very fast for $\left|q\right|<1$. See Chapter 16, "Jacobian Elliptic Functions and Theta Functions" of Handbook of Mathematical Functions edited by Abramowitz and Stegun for more extensive information.

$\mathrm{JacobiTheta1}\left(2.0\&comma;0.5\right)$

$1.632025903$

$\mathrm{JacobiTheta2}\left(2.0\&comma;0.5\right)$

$\mathrm{-0.3181628217}$

$\mathrm{JacobiTheta3}\left(2.0\&comma;0.5\right)$

$0.3314359783$

$\mathrm{JacobiTheta4}\left(2.0\&comma;0.5\right)$

$1.632130562$