查看“︁安格尔函数”︁的源代码

[[File:Anger function 2d.gif|thumb|Anger function  2D animiation]]
[[File:Anger function Maple animation.gif|thumb|AngerJ(v,x) Maple animation for   v=5]]
[[File:Anger function 3d.png|thumb|Anger function  3D plot]]
'''安格尔函数'''是英国数学家安格尔在1855年首先研究的积分函数

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

==微分方程==
安格尔函数满足下列微分方程

:<math>z^2y^{\prime\prime} + zy^\prime +(z^2-\nu^2)y = (z-\nu)\sin(\pi z)/\pi</math>

==参考文献==
*C.T. Anger, Neueste Schr. d. Naturf. d. Ges. i. Danzig, 5  (1855)  pp.&nbsp;1–29
*{{dlmf|id=11.10|title=Anger-Weber Functions|first=R. B. |last=Paris}}
*{{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

[[Category:特殊函数]]