Special Functions of Mathematical Physics and Chemistry |
Contents
CHAPTER | 1 |
Ordinary points of a linear differential equation | 4 |
Regular singular points | 6 |
Copyright | |
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Common terms and phrases
arbitrary constants associated Laguerre polynomials Bessel coefficients Bessel functions corresponding Deduce defined by equation denotes derived differentiate both sides Dirac delta function duplication formula dx2 x dx equation d2R equivalent example expression F₁ follows from equation function J(x gamma function generalisation H₁(x Hence Hermite functions hypergeometric series indicial equation integral J₁(x J₂(x Jn(x Jo(x Laguerre polynomials Laplace's equation Legendre polynomial Legendre's equation mathematical physics normalised obtain the relation P(cos polynomial of degree positive integer problems Prove readily shown recurrence relation regular singular point required solution respect result right-hand side 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 wave mechanics write y₁(x Yo(x αμ Απ µ² πχ