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SERIES SOLUTION OF DIFFERENTIAL EQUATIONS
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Bessel functions Bessel polynomials Bessel's equation boundary conditions boundary-value problem Chapter Chebyshev polynomials Chebyshev's equation consider constant converges uniformly coordinates cosh defined derivative differential equation eigenvalues example expansion expression Find finite formula Fourier series Fourier transform function f(x gamma function given in Exercise half-range hence Hermite polynomials Hermite's Hn(x infinite series integer integral interval inverse transform Jn(x Laguerre polynomials Laplace transform Laplace's equation Legendre polynomials Legendre's equation linearly independent method of Frobenius multiplying non-negative integer norm obtain orthogonal set orthogonality relation Parseval's Pn(x Pnm(x polynomial of degree polynomial solution properties Qn(x recurrence relation result Rodrigues satisfies sectionally continuous separation of variables series solution set f>n(x Show sine Sn(x Solve Exercise special functions Sturm-Liouville Substituting theorem Tn(x Un(x valid values wave equation write Wronskian yields Yn(x zero