Special.HankelH1Scaled Method

Evaluates the Hankel function of the first kind of real order and complex argument and complex argument scaled to remove the exponential factor along the imaginary axis.

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.6
C#
public static Complex<double> HankelH1Scaled(
	double nu,
	Complex<double> z
)

Parameters

nu  Double
A real number that specifies the order of the Bessel function.
z  Complex<Double>
The value at which to evaluate the function.

Return Value

Complex<Double>
The value of the Hankel function of the first kind of order nu at z.

Remarks

The Hankel functions are linear combinations of Bessel functions of the first and second kind. These functions increase exponentially as the imaginary part of the argument increases. This function returns the Hankel function of the second kind scaled by a factor of exp(-|Im(z)|) to remove this exponential factor.

For real z, the scale factor is 1 so the scaled function is identical to the original.

See Also