Higher Transcendental Functions, Volume 2McGraw-Hill, 1953 - Transcendental functions |
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Page 268
... recurrence relation , expressing ( ax + by ) P ; ( x , y ) as a linear combination of polynomials of degree n + 1 ... recurrence relations ; nor does it seem to be known under what conditions a system of poly- nomials satisfying a ...
... recurrence relation , expressing ( ax + by ) P ; ( x , y ) as a linear combination of polynomials of degree n + 1 ... recurrence relations ; nor does it seem to be known under what conditions a system of poly- nomials satisfying a ...
Page 387
... recurrence relation for , 193 relation to parabolic cylinder functions , 117 Rodrigues ' formula for , 193 series of , 193 ff . , 216 zeros of , 204 ff . Hermite polynomials of several variables , 283 ff . Hurwitz's theorem on zeros of ...
... recurrence relation for , 193 relation to parabolic cylinder functions , 117 Rodrigues ' formula for , 193 series of , 193 ff . , 216 zeros of , 204 ff . Hermite polynomials of several variables , 283 ff . Hurwitz's theorem on zeros of ...
Page 389
... formula for , 197 inequalities for , 205 ff . integral representations of , 182 monotonic properties of , 208 recurrence relation for , 179 series of , 182 ff . , 214 Legendre's relation , 320 , 329 Lemniscate functions 320 , 376 Line ...
... formula for , 197 inequalities for , 205 ff . integral representations of , 182 monotonic properties of , 208 recurrence relation for , 179 series of , 182 ff . , 214 Legendre's relation , 320 , 329 Lemniscate functions 320 , 376 Line ...
Contents
BESSEL FUNCTIONS | 1 |
Modified Bessel functions of integer order | 9 |
4 | 22 |
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½ π ½µ ½π a₁ addition theorem Akad algebraic Amer Bessel functions coefficients complex convergence corresponding cosh defined denotes derived differential equation elliptic integrals Erdélyi expressed in terms finite formulas ƒª Gegenbauer Gegenbauer polynomials given H₂ harmonic polynomial hence Hermite polynomials hypergeometric functions integral representations J₂ Jacobi polynomials Jacobian elliptic functions Ju+n Koschmieder Laguerre polynomials Legendre Legendre's London Math Meijer nomials notation obtain orthogonal polynomials poles polynomial of degree Proc proved rational function recurrence relation second kind sin² sinh surface harmonics Szegő theory theta functions third kind transformation Tricomi values variable Watson Weierstrass weight function г ½