using System;
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using Complex = System.Numerics.Complex;
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namespace IStation.Numerics
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{
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/// <summary>
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/// This partial implementation of the SpecialFunctions class contains all methods related to the spherical Bessel functions.
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/// </summary>
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public static partial class SpecialFunctions
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{
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/// <summary>
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/// Returns the spherical Bessel function of the first kind.
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/// <para>SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).</para>
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/// </summary>
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/// <param name="n">The order of the spherical Bessel function.</param>
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/// <param name="z">The value to compute the spherical Bessel function of.</param>
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/// <returns>The spherical Bessel function of the first kind.</returns>
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public static Complex SphericalBesselJ(double n, Complex z)
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{
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if (double.IsNaN(n) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
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{
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return new Complex(double.NaN, double.NaN);
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}
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if (double.IsInfinity(z.Real))
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{
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return (z.Imaginary == 0) ? Complex.Zero : new Complex(double.PositiveInfinity, double.PositiveInfinity);
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}
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if (z.Real == 0 && z.Imaginary == 0)
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{
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return (n == 0) ? 1 : 0;
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}
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return Constants.SqrtPiOver2 * BesselJ(n + 0.5, z) / Complex.Sqrt(z);
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}
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/// <summary>
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/// Returns the spherical Bessel function of the first kind.
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/// <para>SphericalBesselJ(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselJ(n + 1/2, z).</para>
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/// </summary>
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/// <param name="n">The order of the spherical Bessel function.</param>
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/// <param name="z">The value to compute the spherical Bessel function of.</param>
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/// <returns>The spherical Bessel function of the first kind.</returns>
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public static double SphericalBesselJ(double n, double z)
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{
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if (double.IsNaN(n) || double.IsNaN(z))
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{
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return double.NaN;
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}
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if (n < 0)
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{
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return double.NaN;
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}
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if (double.IsInfinity(z))
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{
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return 0;
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}
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if (z == 0)
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{
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return (n == 0) ? 1 : 0;
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}
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return Constants.SqrtPiOver2 * BesselJ(n + 0.5, z) / Math.Sqrt(z);
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}
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/// <summary>
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/// Returns the spherical Bessel function of the second kind.
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/// <para>SphericalBesselY(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselY(n + 1/2, z).</para>
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/// </summary>
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/// <param name="n">The order of the spherical Bessel function.</param>
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/// <param name="z">The value to compute the spherical Bessel function of.</param>
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/// <returns>The spherical Bessel function of the second kind.</returns>
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public static Complex SphericalBesselY(double n, Complex z)
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{
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if (double.IsNaN(n) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
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{
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return new Complex(double.NaN, double.NaN);
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}
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if (double.IsInfinity(z.Real))
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{
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return (z.Imaginary == 0) ? Complex.Zero : new Complex(double.PositiveInfinity, double.PositiveInfinity);
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}
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if (z.Real == 0 && z.Imaginary == 0)
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{
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return new Complex(double.NaN, double.NaN);
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}
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return Constants.SqrtPiOver2 * BesselY(n + 0.5, z) / Complex.Sqrt(z);
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}
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/// <summary>
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/// Returns the spherical Bessel function of the second kind.
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/// <para>SphericalBesselY(n, z) is given by Sqrt(pi/2) / Sqrt(z) * BesselY(n + 1/2, z).</para>
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/// </summary>
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/// <param name="n">The order of the spherical Bessel function.</param>
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/// <param name="z">The value to compute the spherical Bessel function of.</param>
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/// <returns>The spherical Bessel function of the second kind.</returns>
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public static double SphericalBesselY(double n, double z)
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{
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if (double.IsNaN(n) || double.IsNaN(z))
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{
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return double.NaN;
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}
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if (n < 0)
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{
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return double.NaN;
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}
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if (double.IsInfinity(z))
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{
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return 0;
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}
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if (z == 0)
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{
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return double.NegativeInfinity;
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}
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return Constants.SqrtPiOver2 * BesselY(n + 0.5, z) / Math.Sqrt(z);
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}
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}
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}
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