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## Main Question or Discussion Point

I have an awful memory when it comes to factoids, I need to remember the Legendre, Hermite, Laguerre, Chebyshev, Hypergeometric & Jacobi equations, all of which are of the form [itex]p(x)y'' + q(x)y' + r(x)y = 0[/itex], where [itex]p[/itex] is a second degree polynomial, [itex]q[/itex] is a first degree polynomial & [itex]r[/itex] is a zero'th degree polynomial (interpreted as an eigenvalue).

Now, I can derive [itex]r(x)[/itex] by following Arfken's development & just substituting in a series solution & deriving what the eigenvalue should be.

Thus I'm left with finding out a way to remember the coefficients [itex]p(x)[/itex] & [itex]q(x)[/itex] for the Legendre, Hermite, Laguerre, Chebyshev, Hypergeometric & Jacobi equations. Is there any simple way to do this? Any unifying procedure or thought process?

Considering that this question could have been asked by including the [itex]r(x)[/itex] term, would you have recommended subbing in the series to derive the eigenvalue, or just told me to remember them all? :tongue:

I won't start asking about ways to remember things like Bessel's equation, Weber, Matthieu, Lame etc... as I feel that is a fruitless task, though any nice ideas or tips on these monstrosities would be greatly appreciated

Now, I can derive [itex]r(x)[/itex] by following Arfken's development & just substituting in a series solution & deriving what the eigenvalue should be.

Thus I'm left with finding out a way to remember the coefficients [itex]p(x)[/itex] & [itex]q(x)[/itex] for the Legendre, Hermite, Laguerre, Chebyshev, Hypergeometric & Jacobi equations. Is there any simple way to do this? Any unifying procedure or thought process?

Considering that this question could have been asked by including the [itex]r(x)[/itex] term, would you have recommended subbing in the series to derive the eigenvalue, or just told me to remember them all? :tongue:

I won't start asking about ways to remember things like Bessel's equation, Weber, Matthieu, Lame etc... as I feel that is a fruitless task, though any nice ideas or tips on these monstrosities would be greatly appreciated