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Anger function : ウィキペディア英語版
Anger function
In mathematics, the Anger function, introduced by , is a function defined as
: \mathbf_\nu(z)=\frac \int_0^\pi \cos (\nu\theta-z\sin\theta) \,d\theta
and is closely related to Bessel functions.
The Weber function (also known as Lommel-Weber function), introduced by , is a closely related function defined by
: \mathbf_\nu(z)=\frac \int_0^\pi \sin (\nu\theta-z\sin\theta) \,d\theta
and is closely related to Bessel functions of the second kind.
==Relation between Weber and Anger functions==

The Anger and Weber functions are related by
:\sin(\pi \nu)\mathbf_\nu(z) = \cos(\pi\nu)\mathbf_\nu(z)-\mathbf_(z)
:-\sin(\pi \nu)\mathbf_\nu(z) = \cos(\pi\nu)\mathbf_\nu(z)-\mathbf_(z)
so in particular if ν is not an integer they can be expressed as linear combinations of each other. If ν is an integer then Anger functions Jν are the same as Bessel functions ''J''ν, and Weber functions can be expressed as finite linear combinations of Struve functions.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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