Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
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 Associated Laguerre polynomials      176 Associated Laguerre polynomials, definition of      176 Associated Laguerre polynomials, generating function for      177 Associated Laguerre polynomials, notation for      182 Associated Laguerre polynomials, orthogonality properties of      178 Associated Laguerre polynomials, recurrence relations for      178 Associated Legendre equation      62 Associated Legendre functions      62 Associated Legendre functions, definition of      62 Associated Legendre functions, orthogonality relations for      66 Associated Legendre functions, properties of      65 Associated Legendre functions, recurrence relations for      68 Bessel functions      92 Bessel functions of the first kind      94 Bessel functions of the first kind, asymptotic behaviour of      127 Bessel functions of the first kind, definition of      94 Bessel functions of the first kind, generating function for      99 Bessel functions of the first kind, graph of      134 Bessel functions of the first kind, integral representations for      101 Bessel functions of the first kind, orthogonality properties of      137 Bessel functions of the first kind, recurrence relations for      104 Bessel functions of the second kind      97 Bessel functions of the second kind, asymptotic behaviour of      127 Bessel functions of the second kind, definition of      97 Bessel functions of the second kind, explicit expression for      98 Bessel functions of the second kind, graph of      134 Bessel functions of the second kind, recurrence relations for      106 Bessel functions of the third kind      see Hankel functions Bessel series      141 Bessel's equation      92 beta function      23 Beta function, definition of      23 Chebyshev polynomials      187 Chebyshev polynomials, definition of      187 Chebyshev polynomials, generating function for      190 Chebyshev polynomials, orthogonality properties of      192 Chebyshev polynomials, recurrence relations for      193 Chebyshev polynomials, series for      188 Chebyshev polynomials, special values of      192 Chebyshev's equation      189 Confluent hypergeometric equation      210 212 Confluent hypergeometric function      203 Confluent hypergeometric function, contiguity relations for      212 Confluent hypergeometric function, definition of      203 Confluent hypergeometric function, integral representation of      211 Cosine integral      219 Debye functions      224 Differential equations satisfied by various special functions      233 Differential equations, solution of by Frobenius' method      1 Elliptic integrals      224 Error function      221 Euler's constant      231 Exponential integral      218 Fresnel integrals      221 Frobenius' method      1 Frobenius' method, summary of      7 Gamma function      23 Gamma function, definition of      23 30 Gamma function, graph of      31 Gauss's equation      207 Gegenbauer polynomials      197 Gegenbauer polynomials, definition of      197 Gegenbauer polynomials, differential equation satisfied by      198 Gegenbauer polynomials, generating function for      197 Gegenbauer polynomials, orthogonality properties of      198 Gegenbauer polynomials, power series for      198 Gegenbauer polynomials, recurrence relations for      198 Generating function      236 Generating function for associated Laguerre polynomials      177 Generating function for Bessel functions of the first kind      99 Generating function for Chebyshev polynomials      190 Generating function for Gegenbauer polynomials      197 Generating function for Hermite polynomials      157 Generating function for Jacobi polynomials      198 Generating function for Laguerre polynomials      169 Generating function for Legendre polynomials      46 Hankel functions      107 Hankel functions, asymptotic behaviour of      127 Hankel functions, definition of      107 Hankel functions, recurrence relations for      108 Hermite polynomials      156 Hermite polynomials, definition of      157 Hermite polynomials, generating function for      157 Hermite polynomials, orthogonality properties of      161 Hermite polynomials, recurrence relations for      162 Hermite polynomials, special values of      160 Hermite's equation      156 Hypergeometric equation      207 208 Hypergeometric functions      203 Hypergeometric functions, contiguity relations for      210 Hypergeometric functions, definition of      203 Hypergeometric functions, integral representation of      207 Hypergeometric functions, relationship with other special functions      204 Incomplete gamma functions      218 Indicial equation      3 Integral representation of Bessel functions      101 Integral representation of confluent hypergeometric function      211 Integral representation of hypergeometric function      207 Integral representation of Legendre polynomials      49 Integral representation of modified Bessel functions      116 Integrals involving Bessel functions      141 Jacobi polynomials      198 Jacobi polynomials definition of      198 Jacobi polynomials, differential equation satisfied by      199 Jacobi polynomials, generating function for      198 Jacobi polynomials, orthogonality properties of      199 Jacobi polynomials, recurrence relations for      199 Jacobi polynomials, series for      199 Kelvin's functions      120 Kelvin's functions, graphs of      137 Kummer function      204 Kummer's equation      210 l'Hopital's rule      39 97 Laguerre polynomials      168 Laguerre polynomials, definition of      169 Laguerre polynomials, generating function for      169 Laguerre polynomials, notation for      182 Laguerre polynomials, orthogonality properties of      172 Laguerre polynomials, recurrence relations for      173 Laguerre polynomials, special values of      171 Laguerre's equation      168 Laplace's integral representation      49 Legendre duplication formula      29 Legendre functions of the second kind      70 Legendre functions of the second kind, graphs of      84 85 Legendre functions of the second kind, properties of      77 Legendre polynomials      42 Legendre polynomials, definition of      46 Legendre polynomials, generating function for      46 Legendre polynomials, graphs of      82 83 84 Legendre polynomials, Laplace's integral representation for      49 Legendre polynomials, orthogonality properties of      52 Legendre polynomials, recurrence relations for      58 Legendre polynomials, Rodrigues' formula for      48 Legendre polynomials, special values of      50 Legendre series      55 Legendre's associated equation      62 Legendre's equation      42 Leibniz's theorem      63 Logarithmic integral      219 Modified Bessel functions      110 Modified Bessel functions, asymptotic behaviour of      128 Modified Bessel functions, graphs of      135 Modified Bessel functions, integral representations for      116 Modified Bessel functions, recurrence relations for      113 Neumann functions      see Bessel functions of the second kind Neumann's formula      78 Orthogonality properties      234 Orthogonality properties of associated Laguerre polynomials      178 Orthogonality properties of associated Legendre functions      66 Orthogonality properties of Bessel functions      137 Orthogonality properties of Chebyshev polynomials      192 Orthogonality properties of Gegenbauer polynomials      198 Orthogonality properties of Hermite polynomials      161 Orthogonality properties of Jacobi polynomials      199 Orthogonality properties of Laguerre polynomials      172 Orthogonality properties of Legendre polynomials      52 Orthogonality properties of spherical harmonics      80 Pochhammer symbol      203 Rayleigh's formulae      126 Recurrence relations for associated Laguerre polynomials      178 Recurrence relations for associated Legendre functions      68 Recurrence relations for Bessel functions of the first kind      104 Recurrence relations for Bessel functions of the second kind      106 Recurrence relations for Chebyshev polynomials      193 Recurrence relations for Gegenbauer polynomials      198 Recurrence relations for Hankel functions      108 Recurrence relations for Hermite polynomials      162 Recurrence relations for Jacobi polynomials      199 Recurrence relations for Laguerre polynomials      173 Recurrence relations for Legendre polynomials      58 Recurrence relations for modified Bessel functions      113 Recurrence relations for spherical Bessel functions      122 Riemann's zeta function      223 Rodrigues' formula      48 Sine integral      219 Spherical Bessel functions      121 Spherical Bessel functions, asymptotic behaviour of      128 Spherical Bessel functions, graphs of      136 Spherical Bessel functions, Rayleigh's formulae for      126 Spherical Bessel functions, recurrence relations for      122 Spherical harmonics      78 Spherical harmonics, orthogonality properties of      80 Ultraspherical polynomials      see Gegenbauer polynomials Weber — Hermite functions      163 Whittaker's confluent hypergeometric functions      212 Zeta function      223 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2022 | | О проекте