theta-functions-1.0.1: Theta-functions implemented as trigonometric series

Safe Haskell Safe-Infered

Numeric.Functions.Theta

Description

Theta-functions implemented on top of trigonometric series.

Theta-functions are special functions of several complex variables Their importance is that we can construct an elliptic functions from combination of theta-functions, see details at http://en.wikipedia.org/wiki/Theta_function.

Depend on parameter Tau, which should be positive. Call every function in the following form:

`theta1 N (qpar Tau) U`

where `N` is a number of addends in series representing the function, `Tau` is a tau parameter defining the theta-function and `U` is an argument, which is a complex number.

WARNING: theta-functions are raising their values very quickly when arg is raising. This depends on behaviour of cos and sin of complex functions, which are very rapidly increasing their values. Call theta-functions with n < 20, q < 1, |u| < pi.

Synopsis

Documentation

qpar :: RealFloat a => a -> Complex aSource

Theta-function depends on parameter q, which abs should be lower than 1 Parameter q, however, depends on the main parameter tau, so we will make q dependent variable

theta1 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex aSource

Theta_1

theta2 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex aSource

Theta_2

theta3 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex aSource

Theta_3

theta4 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex aSource

Theta_4