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Bessel and Legendre

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1).The Bessel functions Jp satisfy the equations (see attached file) . Use this to show that Bessel functions satisfy Bessel's differential equation. 2) The legendre polynomials satisfy... (see attached) where Pn(x) is the Legendre polynomial of degree n. Show that the Legendre satisfy Legendre's differential equation, (see attached)

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Solution Summary

This provides an example of working with a Bessel's differential equation proof and a Legendre's differential equation proof

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The solution is attached.

Taking equation 2 with p-1 gives

Taking the derivative of ...

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