# 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 This solution is **FREE** courtesy of BrainMass!

The solution is attached.

Taking equation 2 with p-1 gives

Taking the derivative of equation 1 gives

Comparing the right hand sides,

Rearranging, we see that

Thus the Bessel Functions solve Bessel's equation.

Taking the derivative of equation 4,

From equation 3, we see that . Substituting this in gives

Thus the Legendre polynomials satisfy Legendre's equation.

Â© BrainMass Inc. brainmass.com October 5, 2022, 6:17 pm ad1c9bdddf>https://brainmass.com/math/calculus-and-analysis/bessel-functions-legendre-polynomials-215059