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Ordinary points of a linear differential equation
Regular singular points
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arbitrary constants Bessel coefficients Bessel functions coefficients cr coefficients of h corresponding cos2 D. E. Rutherford D.Sc Deduce defined by equation denotes derive differentiate both sides Dirac delta function duplication formula E. W. Hobson equation 8.1 equivalent example expression follows from equation gamma function generalisation Hence Hermite functions Hn(x hypergeometric equation hypergeometric function hypergeometric series indicial equation Jn(x Jv(x Laguerre polynomials Laplace's equation Legendre polynomial Legendre's associated equation Legendre's equation mathematical physics Neumann's formula normalised obtain the relation Ordinary Differential Equations ordinary point orthogonal point at infinity polynomial of degree positive integer possesses solutions properties Prove readily shown recurrence relation regular singular point required solution respect result right-hand side second kind second solution sides of equation Similarly sin2 solution of equation solution of Laplace's solution of Legendre's spherical Substituting theorem variation wave function write yi(x