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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