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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)

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

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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.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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

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