Safe Haskell | Safe-Infered |
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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.

- qpar :: RealFloat a => a -> Complex a
- theta1 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex a
- theta2 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex a
- theta3 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex a
- theta4 :: RealFloat a => Integer -> Complex a -> Complex a -> Complex a