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  "body": "\n## Summary\n\nThe Anger function $\\mathbf{J}_\\nu$ is the function obtained by using Bessel's integral formula for an arbitrary order $\\nu$.\nFor integer $\\nu$ it equals the [[Bessel function of the first kind|CZCMRDWDYW]] $J_\\nu$; for other $\\nu$ it does not.\nIts companion is the Weber function $\\mathbf{E}_\\nu$, defined with a sine in place of the cosine.\nBoth solve inhomogeneous forms of Bessel's equation.\n\n## Explanations\n\n### L1 human\n\nBessel found that $J_n(z)$ is the average of $\\cos(n\\tau - z\\sin\\tau)$ over $0 \\le \\tau \\le \\pi$ when $n$ is a whole number.\nOne can compute the same average when $n$ is replaced by any number $\\nu$.\nThe result is the Anger function.\nWhen $\\nu$ is not a whole number, it is no longer a Bessel function, which shows that Bessel's integral is special to integer orders.\n",
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