/// <summary>
/// Modified Bessel function of the first kind, I(v, z).
/// <p/>
/// If expScaled is true, returns Exp(-Abs(x)) * I(v, z) where x = z.Real.
/// </summary>
/// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns>
public static double BesselI(double v, double z, bool expScaled = false)
{
if (expScaled)
{
return(Amos.ScaledCbesi(v, z));
}
else
{
return(BesselI(v, new Complex(z, 0), expScaled).Real);
}
}
/// <summary>
/// Derivative of the Airy function Ai.
/// <p/>
/// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z).
/// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns>
public static double AiryAiPrime(double z, bool expScaled = false)
{
if (expScaled)
{
return(Amos.ScaledCairyPrime(z));
}
else
{
return(AiryAiPrime(new Complex(z, 0), expScaled).Real);
}
}
/// <summary>
/// Returns the exponentially scaled Airy function Ai.
/// <para>ScaledAiryAi(z) is given by Exp(zta) * AiryAi(z), where zta = (2/3) * z * Sqrt(z).</para>
/// </summary>
/// <param name="z">The value to compute the Airy function of.</param>
/// <returns>The exponentially scaled Airy function Ai.</returns>
public static Complex AiryAiScaled(Complex z)
{
return(Amos.ScaledCairy(z));
}
/// <summary>
/// Returns the Airy function Ai.
/// <para>AiryAi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
/// </summary>
/// <param name="z">The value to compute the Airy function of.</param>
/// <returns>The Airy function Ai.</returns>
public static Complex AiryAi(Complex z)
{
return(Amos.Cairy(z));
}
/// <summary>
/// Returns the Airy function Bi.
/// <para>AiryBi(z) is a solution to the Airy equation, y'' - y * z = 0.</para>
/// </summary>
/// <param name="z">The value to compute the Airy function of.</param>
/// <returns>The Airy function Bi.</returns>
public static Complex AiryBi(Complex z)
{
return(Amos.Cbiry(z));
}
/// <summary>
/// Returns the Bessel function of the second kind.
/// <para>BesselY(n, z) is a solution to the Bessel differential equation.</para>
/// </summary>
/// <param name="n">The order of the Bessel function.</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <returns>The Bessel function of the second kind.</returns>
public static Complex BesselY(double n, Complex z)
{
return(Amos.Cbesy(n, z));
}
/// <summary>
/// Returns the exponentially scaled Bessel function of the first kind.
/// <para>ScaledBesselJ(n, z) is given by Exp(-Abs(z.Imaginary)) * BesselJ(n, z).</para>
/// </summary>
/// <param name="n">The order of the Bessel function.</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <returns>The exponentially scaled Bessel function of the first kind.</returns>
public static double BesselJScaled(double n, double z)
{
return(Amos.ScaledCbesj(n, z));
}
/// <summary>
/// Returns the exponentially scaled derivative of Airy function Ai
/// <para>ScaledAiryAiPrime(z) is given by Exp(zta) * AiryAiPrime(z), where zta = (2/3) * z * Sqrt(z).</para>
/// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <returns>The exponentially scaled derivative of Airy function Ai.</returns>
public static Complex AiryAiPrimeScaled(Complex z)
{
return(Amos.ScaledCairyPrime(z));
}
/// <summary>
/// Hankel function of the second kind, H2(n, z).
/// <p/>
/// If expScaled is true, returns Exp(z * j) * H2(n, z) where j = Sqrt(-1).
/// </summary>
/// <param name="n">The order of the Hankel function</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param>
/// <returns></returns>
public static Complex HankelH2(double n, Complex z, bool expScaled = false)
{
return((expScaled) ? Amos.ScaledCbesh2(n, z) : Amos.Cbesh2(n, z));
}
/// <summary>
/// Returns the exponentially scaled Hankel function of the second kind.
/// <para>ScaledHankelH2(n, z) is given by Exp(z * j) * HankelH2(n, z) where j = Sqrt(-1).</para>
/// </summary>
/// <param name="n">The order of the Hankel function.</param>
/// <param name="z">The value to compute the Hankel function of.</param>
/// <returns>The exponentially scaled Hankel function of the second kind.</returns>
public static Complex HankelH2Scaled(double n, Complex z)
{
return(Amos.ScaledCbesh2(n, z));
}
/// <summary>
/// Returns the Hankel function of the second kind.
/// <para>HankelH2(n, z) is defined as BesselJ(n, z) - j * BesselY(n, z).</para>
/// </summary>
/// <param name="n">The order of the Hankel function.</param>
/// <param name="z">The value to compute the Hankel function of.</param>
/// <returns>The Hankel function of the second kind.</returns>
public static Complex HankelH2(double n, Complex z)
{
return(Amos.Cbesh2(n, z));
}
/// <summary>
/// Modified Bessel function of the first kind, I(v, z).
/// <p/>
/// If expScaled is true, returns Exp(-Abs(x)) * I(v, z) where x = z.Real.
/// </summary>
/// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns>
public static Complex BesselI(double v, Complex z, bool expScaled = false)
{
return((expScaled) ? Amos.ScaledCbesi(v, z) : Amos.Cbesi(v, z));
}
/// <summary>
/// Bessel function of the second kind, Y(v, z).
/// <p/>
/// If expScaled is true, returns Exp(-Abs(y)) * Y(v, z) where y = z.Imaginary.
/// </summary>
/// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns>
public static double BesselY(double v, double z, bool expScaled = false)
{
return((expScaled) ? Amos.ScaledCbesy(v, z) : Amos.Cbesy(v, z));
}
/// <summary>
/// Airy function Bi(z).
/// <p/>
/// If expScaled is true, returns Exp(-axzta) * Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real).
/// </summary>
/// <param name="z">The value to compute the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns>
public static Complex AiryBi(Complex z, bool expScaled = false)
{
return((expScaled) ? Amos.ScaledCbiry(z) : Amos.Cbiry(z));
}
/// <summary>
/// Returns the exponentially scaled Airy function Ai.
/// <para>ScaledAiryAi(z) is given by Exp(zta) * AiryAi(z), where zta = (2/3) * z * Sqrt(z).</para>
/// </summary>
/// <param name="z">The value to compute the Airy function of.</param>
/// <returns>The exponentially scaled Airy function Ai.</returns>
public static double AiryAiScaled(double z)
{
return(Amos.ScaledCairy(z));
}
/// <summary>
/// Returns the exponentially scaled Bessel function of the first kind.
/// <para>ScaledBesselJ(n, z) is given by Exp(-Abs(z.Imaginary)) * BesselJ(n, z).</para>
/// </summary>
/// <param name="n">The order of the Bessel function.</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <returns>The exponentially scaled Bessel function of the first kind.</returns>
public static Complex BesselJScaled(double n, Complex z)
{
return(Amos.ScaledCbesj(n, z));
}
/// <summary>
/// Returns the derivative of the Airy function Ai.
/// <para>AiryAiPrime(z) is defined as d/dz AiryAi(z).</para>
/// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <returns>The derivative of the Airy function Ai.</returns>
public static Complex AiryAiPrime(Complex z)
{
return(Amos.CairyPrime(z));
}
/// <summary>
/// Returns the Bessel function of the first kind.
/// <para>BesselJ(n, z) is a solution to the Bessel differential equation.</para>
/// </summary>
/// <param name="n">The order of the Bessel function.</param>
/// <param name="z">The value to compute the Bessel function of.</param>
/// <returns>The Bessel function of the first kind.</returns>
public static double BesselJ(double n, double z)
{
return(Amos.Cbesj(n, z));
}
/// <summary>
/// Returns the exponentially scaled derivative of the Airy function Ai.
/// <para>ScaledAiryAiPrime(z) is given by Exp(zta) * AiryAiPrime(z), where zta = (2/3) * z * Sqrt(z).</para>
/// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <returns>The exponentially scaled derivative of the Airy function Ai.</returns>
public static double AiryAiPrimeScaled(double z)
{
return(Amos.ScaledCairyPrime(z));
}
/// <summary>
/// Derivative of the Airy function Ai.
/// <p/>
/// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z).
/// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns>
public static Complex AiryAiPrime(Complex z, bool expScaled = false)
{
return((expScaled) ? Amos.ScaledCairyPrime(z) : Amos.CairyPrime(z));
}
