Special Functions of Mathematical Physics and Chemistry |
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CHAPTER | 1 |
Ordinary points of a linear differential equation | 4 |
Regular singular points | 6 |
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arbitrary constants associated Laguerre polynomials Bessel coefficients Bessel functions corresponding Deduce defined by equation denotes derived differentiate both sides Dirac delta function dx2 x dx energy equation d2y equivalent example expression follows from equation gamma function generalisation Hence Hermite functions hypergeometric series indicial equation integral J₁(x Jn(x Jo(x Laguerre polynomials Laplace's equation Legendre polynomial Legendre's equation mathematical physics normalised obtain the relation P(cos P₁(u polynomial of degree positive integer problems Prove readily shown recurrence relation regular singular point required solution respect result right-hand side Schrödinger equation second kind 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 y₂(x Yo(x αμ µ² πχ