Special Functions of Mathematical Physics and Chemistry |
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arbitrary constants Bessel coefficients Bessel functions coefficients of h coordinates corresponding cos² D.Sc Deduce defined by equation denotes derive Dirac delta function duplication formula dx2 x dx 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 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 satisfies 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