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 Airy 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 Airy function Ai.
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/// <para>AiryAi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The Airy function Ai.</returns>
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public static Complex AiryAi(Complex z)
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{
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return Amos.Cairy(z);
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}
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/// <summary>
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/// Returns the exponentially scaled Airy function Ai.
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/// <para>ScaledAiryAi(z) is given by Exp(zta) * AiryAi(z), where zta = (2/3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The exponentially scaled Airy function Ai.</returns>
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public static Complex AiryAiScaled(Complex z)
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{
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return Amos.ScaledCairy(z);
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}
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/// <summary>
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/// Returns the Airy function Ai.
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/// <para>AiryAi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The Airy function Ai.</returns>
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public static double AiryAi(double z)
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{
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return AiryAi(new Complex(z, 0)).Real;
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}
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/// <summary>
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/// Returns the exponentially scaled Airy function Ai.
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/// <para>ScaledAiryAi(z) is given by Exp(zta) * AiryAi(z), where zta = (2/3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The exponentially scaled Airy function Ai.</returns>
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public static double AiryAiScaled(double z)
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{
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return Amos.ScaledCairy(z);
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}
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/// <summary>
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/// Returns the derivative of the Airy function Ai.
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/// <para>AiryAiPrime(z) is defined as d/dz AiryAi(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The derivative of the Airy function Ai.</returns>
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public static Complex AiryAiPrime(Complex z)
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{
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return Amos.CairyPrime(z);
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}
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/// <summary>
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/// Returns the exponentially scaled derivative of Airy function Ai
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/// <para>ScaledAiryAiPrime(z) is given by Exp(zta) * AiryAiPrime(z), where zta = (2/3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The exponentially scaled derivative of Airy function Ai.</returns>
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public static Complex AiryAiPrimeScaled(Complex z)
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{
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return Amos.ScaledCairyPrime(z);
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}
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/// <summary>
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/// Returns the derivative of the Airy function Ai.
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/// <para>AiryAiPrime(z) is defined as d/dz AiryAi(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The derivative of the Airy function Ai.</returns>
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public static double AiryAiPrime(double z)
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{
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return AiryAiPrime(new Complex(z, 0)).Real;
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}
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/// <summary>
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/// Returns the exponentially scaled derivative of the Airy function Ai.
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/// <para>ScaledAiryAiPrime(z) is given by Exp(zta) * AiryAiPrime(z), where zta = (2/3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The exponentially scaled derivative of the Airy function Ai.</returns>
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public static double AiryAiPrimeScaled(double z)
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{
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return Amos.ScaledCairyPrime(z);
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}
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/// <summary>
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/// Returns the Airy function Bi.
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/// <para>AiryBi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The Airy function Bi.</returns>
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public static Complex AiryBi(Complex z)
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{
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return Amos.Cbiry(z);
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}
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/// <summary>
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/// Returns the exponentially scaled Airy function Bi.
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/// <para>ScaledAiryBi(z) is given by Exp(-Abs(zta.Real)) * AiryBi(z) where zta = (2 / 3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The exponentially scaled Airy function Bi(z).</returns>
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public static Complex AiryBiScaled(Complex z)
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{
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return Amos.ScaledCbiry(z);
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}
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/// <summary>
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/// Returns the Airy function Bi.
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/// <para>AiryBi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The Airy function Bi.</returns>
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public static double AiryBi(double z)
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{
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return AiryBi(new Complex(z, 0)).Real;
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}
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/// <summary>
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/// Returns the exponentially scaled Airy function Bi.
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/// <para>ScaledAiryBi(z) is given by Exp(-Abs(zta.Real)) * AiryBi(z) where zta = (2 / 3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the Airy function of.</param>
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/// <returns>The exponentially scaled Airy function Bi.</returns>
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public static double AiryBiScaled(double z)
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{
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return AiryBiScaled(new Complex(z, 0)).Real;
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}
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/// <summary>
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/// Returns the derivative of the Airy function Bi.
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/// <para>AiryBiPrime(z) is defined as d/dz AiryBi(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The derivative of the Airy function Bi.</returns>
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public static Complex AiryBiPrime(Complex z)
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{
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return Amos.CbiryPrime(z);
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}
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/// <summary>
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/// Returns the exponentially scaled derivative of the Airy function Bi.
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/// <para>ScaledAiryBiPrime(z) is given by Exp(-Abs(zta.Real)) * AiryBiPrime(z) where zta = (2 / 3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The exponentially scaled derivative of the Airy function Bi.</returns>
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public static Complex AiryBiPrimeScaled(Complex z)
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{
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return Amos.ScaledCbiryPrime(z);
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}
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/// <summary>
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/// Returns the derivative of the Airy function Bi.
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/// <para>AiryBiPrime(z) is defined as d/dz AiryBi(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The derivative of the Airy function Bi.</returns>
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public static double AiryBiPrime(double z)
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{
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return AiryBiPrime(new Complex(z, 0)).Real;
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}
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/// <summary>
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/// Returns the exponentially scaled derivative of the Airy function Bi.
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/// <para>ScaledAiryBiPrime(z) is given by Exp(-Abs(zta.Real)) * AiryBiPrime(z) where zta = (2 / 3) * z * Sqrt(z).</para>
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/// </summary>
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/// <param name="z">The value to compute the derivative of the Airy function of.</param>
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/// <returns>The exponentially scaled derivative of the Airy function Bi.</returns>
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public static double AiryBiPrimeScaled(double z)
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{
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return AiryBiPrimeScaled(new Complex(z, 0)).Real;
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}
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}
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}
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