A Treatise on Special Functions, for Scientists and Engineers |
Contents
SOLUTION OF DIFFERENTIAL EQUATION | 1 |
GAMMA FUNCTION BETA FUNCTION | 33 |
HYPERGEOMETRIC FUNCTION | 52 |
Copyright | |
3 other sections not shown
Common terms and phrases
assume becomes Bessel Functions C₁ C₂ called CHAPTER coefficient of h constants convergent Corollary d2y dx2 day dx2 defined definition denote differential equation dx dx dy dx Equating the coefficient Equating to zero evident Example expansion expression factor formula function given gives Hence Hn(x hypergeometric equation Hypergeometric Function indicial equation integral integrating with respect interval Jn(x known left hand side Legendre polynomials lowest degree term Multiplying obtain P₁ Pn(x polynomial powers properties Prove recurrence relation reduces regular singularity result right hand side roots series solution Show Similarly solution Solve Special Functions stands Substituting term term containing Un+1 values write y₁ zero the coefficient