Anger function: Difference between revisions

Revision as of 18:52, 28 August 2022

Revision as of 14:05, 26 August 2023

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: <math>\mathbf{J}_\nu(z)=\frac{1}{\pi} \int_0^\pi \cos (\nu\theta-z\sin\theta) \,d\theta</math>

*with complex parameter '''v''' and complex variable '''x'''.<ref name="EOM_Anger">{{springer|id=A/a012490|title=Anger function|first=A.P.|last= Prudnikov|authorlink=Anatolii Platonovich Prudnikov}}</ref> It is closely related to the [[Bessel function]]s.

and is closely related to [[Bessel function]]s.

The '''Weber function''' (also known as '''[[Eugen von Lommel|Lommel]]–Weber function'''), introduced by {{harvs|txt|authorlink=Heinrich Friedrich Weber|first=H. F.|last=Weber|year=1879}}, is a closely related function defined by

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==References==

{{Reflist}}

{{Refbegin}}

*{{AS ref|12|498}}

*C.T. Anger, Neueste Schr. d. Naturf. d. Ges. i. Danzig, 5 (1855) pp.&nbsp;1–29

*{{springer|id=A/a012490|title=Anger function|first=A.P.|last= Prudnikov|authorlink=Anatolii Platonovich Prudnikov}}

*{{springer|id=W/w097320|title=Weber function|first=A.P.|last= Prudnikov}}

*[[G.N. Watson]], "A treatise on the theory of Bessel functions", 1–2, Cambridge Univ. Press (1952)

*H.F. Weber, Zurich Vierteljahresschrift, 24 (1879) pp.&nbsp;33–76

{{ReflistRefend}}

[[Category:Special functions]]