Special Functions of Mathematical Physics and Chemistry |
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arbitrary constants Bessel coefficients Bessel functions coefficients of h corresponding D.Sc Deduce defined by equation denotes derive Dirac delta function duplication formula equation 8.1 equivalent example expansion expression F₁ finite follows from equation gamma function generalisation Hence Hermite functions hypergeometric equation hypergeometric series indicial equation integral J₁(x Jn(x Jo(x Laguerre polynomials Laplace's equation Legendre functions Legendre polynomial Legendre's associated equation Legendre's equation mathematical physics normalised obtain the relation orthogonal P(cos P₂(µ polynomial of degree positive integer possesses solutions problems Prove readily shown recurrence relation regular singular point result right-hand side roots Schrödinger equation second solution sides of equation Similarly sin² solution of equation solution of Laplace's solution of Legendre's spherical Substituting theorem values variable variation wave function write y₁(x Yo(x αμ µ² πχ