Numeric.Functions.Theta

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 http://en.wikipedia.org/wiki/Theta_function Depend on parameter tau, which should be positive Call every function as thetaN 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 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

Documentation

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

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 a

Theta_1

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

Theta_2

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

Theta_3

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

Theta_4