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# hankel

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Hankel's asymptotic expansion of large values of \a x
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C++
Excel

## Hankel

 doublehankel( double x double v )
There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) which is a linear combination of Bessel functions of the first and second kinds. These are called the Hankel functions of the first and second kinds. The other type of Hankel function (this one) is defined by the contour integral:

$H_v&space;(x)&space;=&space;\int_{C_v&space;}&space;\frac{(-&space;\omega)^{x-1}&space;e^{-\omega&space;}&space;}{1-e^{-\omega&space;}}&space;d\omega$

for $\inline&space;&space;\Im&space;[\omega]&space;<&space;0$ , $\inline&space;&space;\mid&space;arg(-\omega)&space;\mid&space;<&space;\pi$ , $\inline&space;&space;v&space;\not=&space;2\pi&space;k&space;>&space;0$, where $\inline&space;&space;C_v$ is a Hankel contour.

## References:

Cephes Math Library Release 2.8: June, 2000

### Parameters

 x input argument v order

### Authors

Stephen L. Moshier. Copyright 1984, 1987, 2000
Documentation by Will Bateman (August 2005)
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