# 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

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##### Solution Summary

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

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