JUCE/modules/juce_dsp/maths/juce_SpecialFunctions.h

/*
  ==============================================================================

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   Copyright (c) 2017 - ROLI Ltd.

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  ==============================================================================
*/


/**
    Contains miscellaneous filter design and windowing functions.
*/
struct SpecialFunctions
{
    /** Computes the modified Bessel function of the first kind I0 for a
        given double value x. Modified Bessel functions are useful to solve
        various mathematical problems involving differential equations.
    */
    static double besselI0 (double x) noexcept;

    /** Computes the complete elliptic integral of the first kind K for a
        given double value k, and the associated complete elliptic integral
        of the first kind Kp for the complementary modulus of k.
    */
    static void ellipticIntegralK (double k, double& K, double& Kp) noexcept;

    /** Computes the Jacobian elliptic function cd for the elliptic
        modulus k and the quarter-period units u.
    */
    static Complex<double> cde (Complex<double> u, double k) noexcept;

    /** Computes the Jacobian elliptic function sn for the elliptic
        modulus k and the quarter-period units u.
    */
    static Complex<double> sne (Complex<double> u, double k) noexcept;

    /** Computes the inverse of the Jacobian elliptic function sn
        for the elliptic modulus k and the quarter-period units u.
    */
    static Complex<double> asne (Complex<double> w, double k) noexcept;
};