A Treatise on Special Functions, for Scientists and Engineers |
Contents
SOLUTION OF DIFFERENTIAL EQUATION | 1 |
GAMMA FUNCTION BETA FUNCTION | 33 |
HYPERGEOMETRIC FUNCTION | 52 |
Copyright | |
2 other sections not shown
Common terms and phrases
A₁ ascending powers aẞy Bessel Functions C₁ C₂ coefficient of xº Confluent Hypergeometric Function convergent Corollary d2y dx2 dy d2y dy denote differential equation dx dx dx dx2 dy dx dy dz dz2 dz e-xx Equating the coefficient Equating to zero erfx expansion expression Gamma function Hermite polynomial Hn(x hypergeometric equation hypergeometric series indicial equation integer integrating with respect Jn(x left hand side Legendre polynomials Legendre's Legendre's equation lowest degree term obtain P₁ P₁(x Pn(x positive integer recurrence relation regular singularity right hand side satisfies the equation series solution singular point Solve in series Special Functions Substituting these results term containing Un+1 W₁ Whittaker functions xn+1 xp(x y₁ zero the coefficient αβ Ип Сохо хп