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    Besell's Equation

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    Bessel's Equation:

    (a) x^2y" + xy' + (x^2 - n^2)y = 0.

    Write the solution as:

    (b) y(x) = Sum lambda = 0, a_lambda * x ^ (lamda = k)

    Substituting (b) into (a) yields:

    Sum lambda = 0, a_lambda * [(k + lambda)(k + lamdba - 1) + (k + lamdba) - n^2]*x^(k + lamda)
    + Sum lamdba = 0, a_lambda * x ^ (lambda + k + 2)
    = 0

    © BrainMass Inc. brainmass.com March 5, 2021, 12:24 am ad1c9bdddf
    https://brainmass.com/physics/power/besell-equation-504948

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    We are given Bessel's ...

    Solution Summary

    We derive a power series expansion for the nth order Bessel function from Bessel's differential equation.

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