Special Functions of Mathematical Physics and Chemistry |
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Bessel coefficients Bessel functions c₁ coefficients of h coordinates corresponding cos² Deduce defined by equation denotes derive duplication formula E. W. Hobson equation 8.1 equivalent example expansion expression F₁ follows from equation gamma function Hence hypergeometric equation hypergeometric function hypergeometric series indicial equation Jo(x Laguerre polynomials Laplace's equation Legendre functions Legendre polynomial Legendre's associated equation Legendre's equation Legendre's equation 17.1 mathematical physics Neumann's formula normalised obtain the relation orthogonal P(cos P₁(cos polynomial of degree positive integer possesses a solution potential theory problems Prove Qn(µ recurrence relation regular singular point result roots satisfies Schrödinger equation second solution sides of equation Similarly sin² solution of equation solution of Laplace's solution of Legendre's Substituting theorem variable variation wave function write y₁(x Yo(x αμ αξ µ²