diff --git a/api/MathNet.Numerics/SpecialFunctions.htm b/api/MathNet.Numerics/SpecialFunctions.htm index 06b0b418..654cf10b 100644 --- a/api/MathNet.Numerics/SpecialFunctions.htm +++ b/api/MathNet.Numerics/SpecialFunctions.htm @@ -333,6 +333,8 @@
  • KelvinKerPrime
  • Logistic
  • Logit
    • +
  • MarcumQ
    • +
  • MarcumQ
  • Multinomial
  • RisingFactorial
  • SphericalBesselJ
    • @@ -632,41 +634,41 @@
    -

    double AiryBiScaled(double z)

    +

    Complex AiryBiScaled(Complex z)

    Returns the exponentially scaled Airy function Bi.

    ScaledAiryBi(z) is given by Exp(-Abs(zta.Real)) * AiryBi(z) where zta = (2 / 3) * z * Sqrt(z).

    Parameters
    -
    double z
    +
    Complex z

    The value to compute the Airy function of.

    Return
    -
    double
    -

    The exponentially scaled Airy function Bi.

    +
    Complex
    +

    The exponentially scaled Airy function Bi(z).

    -

    Complex AiryBiScaled(Complex z)

    +

    double AiryBiScaled(double z)

    Returns the exponentially scaled Airy function Bi.

    ScaledAiryBi(z) is given by Exp(-Abs(zta.Real)) * AiryBi(z) where zta = (2 / 3) * z * Sqrt(z).

    Parameters
    -
    Complex z
    +
    double z

    The value to compute the Airy function of.

    Return
    -
    Complex
    -

    The exponentially scaled Airy function Bi(z).

    +
    double
    +

    The exponentially scaled Airy function Bi.

    @@ -825,7 +827,7 @@ in each interval.
    -

    Complex BesselJ(double n, Complex z)

    +

    double BesselJ(double n, double z)

    Returns the Bessel function of the first kind.

    BesselJ(n, z) is a solution to the Bessel differential equation.

    @@ -834,20 +836,20 @@ in each interval.
    double n

    The order of the Bessel function.

    -
    Complex z
    +
    double z

    The value to compute the Bessel function of.

    Return
    -
    Complex
    +
    double

    The Bessel function of the first kind.

    -

    double BesselJ(double n, double z)

    +

    Complex BesselJ(double n, Complex z)

    Returns the Bessel function of the first kind.

    BesselJ(n, z) is a solution to the Bessel differential equation.

    @@ -856,13 +858,13 @@ in each interval.
    double n

    The order of the Bessel function.

    -
    double z
    +
    Complex z

    The value to compute the Bessel function of.

    Return
    -
    double
    +
    Complex

    The Bessel function of the first kind.

    @@ -1025,7 +1027,7 @@ of the second kind of order 1 of the argument..
    -

    double BesselKScaled(double n, double z)

    +

    Complex BesselKScaled(double n, Complex z)

    Returns the exponentially scaled modified Bessel function of the second kind.

    ScaledBesselK(n, z) is given by Exp(z) * BesselK(n, z).

    @@ -1034,20 +1036,20 @@ of the second kind of order 1 of the argument..
    double n

    The order of the modified Bessel function.

    -
    double z
    +
    Complex z

    The value to compute the modified Bessel function of.

    Return
    -
    double
    +
    Complex

    The exponentially scaled modified Bessel function of the second kind.

    -

    Complex BesselKScaled(double n, Complex z)

    +

    double BesselKScaled(double n, double z)

    Returns the exponentially scaled modified Bessel function of the second kind.

    ScaledBesselK(n, z) is given by Exp(z) * BesselK(n, z).

    @@ -1056,20 +1058,20 @@ of the second kind of order 1 of the argument..
    double n

    The order of the modified Bessel function.

    -
    Complex z
    +
    double z

    The value to compute the modified Bessel function of.

    Return
    -
    Complex
    +
    double

    The exponentially scaled modified Bessel function of the second kind.

    -

    Complex BesselY(double n, Complex z)

    +

    double BesselY(double n, double z)

    Returns the Bessel function of the second kind.

    BesselY(n, z) is a solution to the Bessel differential equation.

    @@ -1078,20 +1080,20 @@ of the second kind of order 1 of the argument..
    double n

    The order of the Bessel function.

    -
    Complex z
    +
    double z

    The value to compute the Bessel function of.

    Return
    -
    Complex
    +
    double

    The Bessel function of the second kind.

    -

    double BesselY(double n, double z)

    +

    Complex BesselY(double n, Complex z)

    Returns the Bessel function of the second kind.

    BesselY(n, z) is a solution to the Bessel differential equation.

    @@ -1100,21 +1102,21 @@ of the second kind of order 1 of the argument..
    double n

    The order of the Bessel function.

    -
    double z
    +
    Complex z

    The value to compute the Bessel function of.

    Return
    -
    double
    +
    Complex

    The Bessel function of the second kind.

    -

    Complex BesselYScaled(double n, Complex z)

    -
    Returns the exponentially scaled Bessel function of the second kind.

    ScaledBesselY(n, z) is given by Exp(-Abs(z.Imaginary)) * Y(n, z).

    +

    double BesselYScaled(double n, double z)

    +
    Returns the exponentially scaled Bessel function of the second kind.

    ScaledBesselY(n, z) is given by Exp(-Abs(z.Imaginary)) * BesselY(n, z).

    @@ -1122,21 +1124,21 @@ of the second kind of order 1 of the argument..
    double n

    The order of the Bessel function.

    -
    Complex z
    +
    double z

    The value to compute the Bessel function of.

    Return
    -
    Complex
    +
    double

    The exponentially scaled Bessel function of the second kind.

    -

    double BesselYScaled(double n, double z)

    -
    Returns the exponentially scaled Bessel function of the second kind.

    ScaledBesselY(n, z) is given by Exp(-Abs(z.Imaginary)) * BesselY(n, z).

    +

    Complex BesselYScaled(double n, Complex z)

    +
    Returns the exponentially scaled Bessel function of the second kind.

    ScaledBesselY(n, z) is given by Exp(-Abs(z.Imaginary)) * Y(n, z).

    @@ -1144,13 +1146,13 @@ of the second kind of order 1 of the argument..
    double n

    The order of the Bessel function.

    -
    double z
    +
    Complex z

    The value to compute the Bessel function of.

    Return
    -
    double
    +
    Complex

    The exponentially scaled Bessel function of the second kind.

    @@ -1846,22 +1848,22 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    Complex32 Hypotenuse(Complex32 a, Complex32 b)

    +

    float Hypotenuse(float a, float b)

    Numerically stable hypotenuse of a right angle triangle, i.e. (a,b) -> sqrt(a^2 + b^2)
    Parameters
    -
    Complex32 a
    +
    float a

    The length of side a of the triangle.

    -
    Complex32 b
    +
    float b

    The length of side b of the triangle.

    Return
    -
    Complex32
    +
    float

    Returns sqrt(a2 + b2) without underflow/overflow.

    @@ -1890,22 +1892,22 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    float Hypotenuse(float a, float b)

    +

    Complex32 Hypotenuse(Complex32 a, Complex32 b)

    Numerically stable hypotenuse of a right angle triangle, i.e. (a,b) -> sqrt(a^2 + b^2)
    Parameters
    -
    float a
    +
    Complex32 a

    The length of side a of the triangle.

    -
    float b
    +
    Complex32 b

    The length of side b of the triangle.

    Return
    -
    float
    +
    Complex32

    Returns sqrt(a2 + b2) without underflow/overflow.

    @@ -1998,15 +2000,13 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    double KelvinBeiPrime(double nu, double x)

    +

    double KelvinBeiPrime(double x)

    Returns the derivative of the Kelvin function bei.
    Parameters
    -
    double nu
    -

    The order of the Kelvin function.

    double x

    The value to compute the derivative of the Kelvin function of.

    @@ -2014,19 +2014,21 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    Return
    double
    -

    the derivative of the Kelvin function bei.

    +

    The derivative of the Kelvin function bei.

    -

    double KelvinBeiPrime(double x)

    +

    double KelvinBeiPrime(double nu, double x)

    Returns the derivative of the Kelvin function bei.
    Parameters
    +
    double nu
    +

    The order of the Kelvin function.

    double x

    The value to compute the derivative of the Kelvin function of.

    @@ -2034,7 +2036,7 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    Return
    double
    -

    The derivative of the Kelvin function bei.

    +

    the derivative of the Kelvin function bei.

    @@ -2082,13 +2084,15 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    double KelvinBerPrime(double x)

    +

    double KelvinBerPrime(double nu, double x)

    Returns the derivative of the Kelvin function ber.
    Parameters
    +
    double nu
    +

    The order of the Kelvin function.

    double x

    The value to compute the derivative of the Kelvin function of.

    @@ -2096,21 +2100,19 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    Return
    double
    -

    The derivative of the Kelvin function ber.

    +

    the derivative of the Kelvin function ber

    -

    double KelvinBerPrime(double nu, double x)

    +

    double KelvinBerPrime(double x)

    Returns the derivative of the Kelvin function ber.
    Parameters
    -
    double nu
    -

    The order of the Kelvin function.

    double x

    The value to compute the derivative of the Kelvin function of.

    @@ -2118,7 +2120,7 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    Return
    double
    -

    the derivative of the Kelvin function ber

    +

    The derivative of the Kelvin function ber.

    @@ -2225,13 +2227,15 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    double KelvinKer(double x)

    -
    Returns the Kelvin function ker.

    KelvinKer(x) is given by the real part of Exp(-nu * pi * j / 2) * BesselK(0, sqrt(j) * x) where j = sqrt(-1).

    KelvinKer(x) is equivalent to KelvinKer(0, x).

    +

    double KelvinKer(double nu, double x)

    +
    Returns the Kelvin function ker.

    KelvinKer(nu, x) is given by the real part of Exp(-nu * pi * j / 2) * BesselK(nu, sqrt(j) * x) where j = sqrt(-1).

    Parameters
    +
    double nu
    +

    the order of the the Kelvin function.

    double x

    The non-negative real value to compute the Kelvin function of.

    @@ -2245,15 +2249,13 @@ see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
    -

    double KelvinKer(double nu, double x)

    -
    Returns the Kelvin function ker.

    KelvinKer(nu, x) is given by the real part of Exp(-nu * pi * j / 2) * BesselK(nu, sqrt(j) * x) where j = sqrt(-1).

    +

    double KelvinKer(double x)

    +
    Returns the Kelvin function ker.

    KelvinKer(x) is given by the real part of Exp(-nu * pi * j / 2) * BesselK(0, sqrt(j) * x) where j = sqrt(-1).

    KelvinKer(x) is equivalent to KelvinKer(0, x).

    Parameters
    -
    double nu
    -

    the order of the the Kelvin function.

    double x

    The non-negative real value to compute the Kelvin function of.

    @@ -2347,6 +2349,40 @@ between 0 and 1.

    The logarithm of p divided by 1.0 - p.

    +
    +
    +
    +

    double MarcumQ(double nu, double a, double b)

    +
    Returns the Marcum Q-function Q[ν](a,b).

    References: A. Gil, J. Segura and N.M. Temme. Efficient and accurate algorithms for the +computation and inversion of the incomplete gamma function ratios. SIAM J Sci Comput. (2012) 34(6), A2965-A2981

    + + +
    +
    Parameters
    + +
    double nu
    +

    The order of generalized Marcum Q-function. Range: 1≦ν≦10000

    +
    double a
    +

    The value to compute the Marcum Q-function of. Range: 0≦a≦10000

    +
    double b
    +

    The value to compute the Marcum Q-function of. Range: 0≦b≦10000

    +
    + +
    +
    Return
    +
    double
    +

    The Marcum Q-function Q[ν](a,b)

    +
    + +
    +
    +
    +

    double MarcumQ(double nu, double a, double b, Int32& err)

    +
    + + + +
    @@ -2386,7 +2422,7 @@ between 0 and 1.

    -

    double SphericalBesselJ(double n, double z)

    +

    Complex SphericalBesselJ(double n, Complex z)

    Returns the spherical Bessel function of the first kind.

    SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).

    @@ -2395,20 +2431,20 @@ between 0 and 1.

    double n

    The order of the spherical Bessel function.

    -
    double z
    +
    Complex z

    The value to compute the spherical Bessel function of.

    Return
    -
    double
    +
    Complex

    The spherical Bessel function of the first kind.

    -

    Complex SphericalBesselJ(double n, Complex z)

    +

    double SphericalBesselJ(double n, double z)

    Returns the spherical Bessel function of the first kind.

    SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).

    @@ -2417,13 +2453,13 @@ between 0 and 1.

    double n

    The order of the spherical Bessel function.

    -
    Complex z
    +
    double z

    The value to compute the spherical Bessel function of.

    Return
    -
    Complex
    +
    double

    The spherical Bessel function of the first kind.