# theta-functions: Theta-functions implemented as trigonometric series

[ library, math, public-domain ] [ Propose Tags ]

Small and simple library for computing values of Theta functions. They're the special functions of two variables. Described very well at https://en.wikipedia.org/wiki/Theta_function. Library exports four theta-functions and a small helper to calculate their second parameter. Theta functions are functions of Complex variables, FYI.

Versions 0.1, 1.0.0, 1.0.1 base (>=4.3.1.0 && <5) [details] LicenseRef-PublicDomain Mark Safronov a.k.a. hijarian hijarian@gmail.com Math https://github.com/hijarian/theta-functions head: git clone git@github.com:hijarian/theta-functions.git by MarkSafronov at Thu Jun 21 06:18:35 UTC 2012 NixOS:1.0.1 1163 total (41 in the last 30 days) (no votes yet) [estimated by rule of succession] λ λ λ Docs uploaded by userBuild status unknown Hackage Matrix CI

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# theta-functions

Implementation of theta-functions using trigonometric series.

They're the special functions of two variables. Described very well at Wikipedia article.

Library exports four theta-functions and a small helper to calculate their second parameter.

Theta functions are functions of Complex variables, FYI.

# Interface summary

thetaN n q u


where N is a number from 1 to 4, n is a quantization factor, q is a theta-functions special parameter, and u is an actual argument of function.

Parameter q should be calculated with the helper function qpar, which accepts real numbers as argument:

qpar tau


qpar itself returns Complex value. This helper is used to draw the library closer to the definition of theta-functions provided in the books.

# Constraints

Never call theta1..4 with u > pi. Theta-functions are raising very rapidly (maybe it's because of trigonometric series representing them), so with large values of argument they overflow badly and return incorrect results.