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Jackson D. Ч Fourier Series and Orthogonal Polynomials
Jackson D. Ч Fourier Series and Orthogonal Polynomials

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Ќазвание: Fourier Series and Orthogonal Polynomials

јвтор: Jackson D.

јннотаци€:

This textbook explains Fourier, Legendre, and Bessel functions for solving the partial differential equations of mathematical physics, applies them to boundary value problems, and introduces three systems of orthogonal polynomials: Jacobi, Hermite, and Laguerre. The Dover edition is an unabridged republication of the work published by The Mathematical Association of America in 1941.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 234

ƒобавлена в каталог: 05.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Asymptotic formula for $J_p(x)$      87Ч88
Bessel functions of order $\pm\dfrac12$      217
Bessel functions of order n      80Ч88 217Ч19
Bessel functions of order zero      69Ч80 216 219
Bessel series      79Ч80 83Ч84 109Ч114 138Ч141 216
Birkhoff, G.D.      90 229
Bocher, M.      24 229
Boundary value problems      88Ч90 91Ч141 220Ч223
Bounds of Legendre polynomials      61Ч63
Bounds of normalized Jacobi polynomials      191Ч92 200Ч201
Bounds of other orthonormal polynomials      201Ч208
Broken-line function      13Ч14 21
Byerly, W.E.      112 220
Carslaw, H.S.      229
Charlier, C      178 179
Christoffel Ч Darboux identity      157Ч58
Christoffel, E.B.      54 55 157 158 206
ChristoffelТs identity      54Ч55
Churchill, R.V.      229
Convergence of Fourier series      12Ч14 18Ч25 42Ч44
Convergence of of Legendre series      63Ч68 215
Convergence of of more general series of orthogonal polynomials      191Ч208
Cosine series      6Ч7 8Ч9
Cosine sum      36
Courant, R.      88 189 229
Cylindrical coordinates      106 109Ч114 138Ч141
Damped vibrations      100Ч101 221
Darboux, G.      157 158 175 206 229
de la Valine Poussin, C.J.      35
de Moivre, A.      126
Derivative formula for Hermite polynomials      176Ч77
Derivative formula for Jacobi polynomials      166Ч167
Derivative formula for Laguerre polynomials      184
Derivative formula for Legendre polynomials      57Ч58
Differential equation for $J_0(x)$      69Ч71 74Ч76 89 219
Differential equation for $J_n(x)$      80Ч82
Differential equation for a class of orthogonal polynomials      161Ч165
Differential equation for derivatives of Legendre polynomials      119Ч120
Differential equation for Hermite polynomials      180 226
Differential equation for Jacobi polynomials      173Ч174 225
Differential equation for Laguerre polynomials      186 226Ч227
Differential equation for Legendre polynomials      48Ч49 55Ч57 88Ч89
Differential equation for Pearson frequency functions      142Ч147
Differential equation for sines and cosines      88
Differential equation for Sturm Ч Liouville functions      89Ч90
Discontinuities      9Ч11 22Ч24 65Ч67
Double Fourier series      115Ч117
Elderton, W.Palin      229
Even function      6Ч7
Fejer, L.      32 229
FejerТs theorem      32Ч35
Finite jump      19
Flow of heat      92
for polynomial approximation      212
Fourier series      1Ч44 91Ч101 103Ч105 111Ч112 115Ч117 209Ч211
Frank, P.      230
Frequency functions      142Ч148 223
Function (general notion)      10
Gauss, K.F.      55
Generating function for Hermite polynomials      181
Generating function for Jacobi polynomials      174Ч75
Generating function for Laguerre polynomials      187Ч188
Generating function for Legendre polynomials      45Ч46
Generating function for ultraspherical polynomials      225Ч26
Gibbs phenomenon      24
Gibbs, T.Willard      24
Gram Ч Charlier series      179
Gram, J.P.      178 179
Gray, A.      229
Green, G.      103 107
Harmonic polynomials      126Ч132 137Ч138
Heine, E.      175
Hermite polynomials      176Ч183 226
Hermite series      178Ч179
Hilbert, D.      88 189 229
Hille, E.      230
Hobson, E.W.      229
Ince, E.L.      90 229
Integrability      5
Integrability in the sense of Lebesgue      5 197Ч99
Integral representation of $J_0(x)$      74Ч76
Integral representation of $J_n(x)$      84Ч85 218
Integral representation of $P_n(x)$      58Ч60
Jackson, D.      44
Jacobi polynomials      166Ч175 200Ч201 225Ч226
Jacobi series      172 201
Kaczmarz, S.      229
Kellogg, O.D.      229
Korous, J.      205
Laguerre polynomials      184Ч190 226Ч227
Laguerre series      186
Laplace series      121Ч138 222
LaplaceТs equation      91Ч96 101Ч112 115Ч141 220Ч222
Leading coefficients of Hermite polynomials      177
Leading coefficients of Jacobi polynomials      169Ч171 172
Leading coefficients of Laguerre polynomials      184
Leading coefficients of Legendre polynomials      47Ч48
Least-square property of Fourier series      27Ч29
Least-square property of general orthogonal polynomials      160Ч161
Least-square property of Legendre series      215Ч216
Lebesgue constants      40Ч42
Lebesgue, H.      5 40 41 42 43 44 196 197 229
Legendre polynomials      45Ч68 213Ч216
Legendre series      53 63Ч68 107Ч209 214Ч16
Leibniz, G.W.      166 167 169 184 186 187
Liouville, J.      89
Lipschitz, R.      44
Mac Lane, S.      viii
Maclaurin, C.      49
MacRobert, T.M.      229
Marden, M.      162
Mathews, G.B.      229
Moments      144Ч48
Moore, C.N.      84
Normalizing factor for Bessel functions      73Ч74 83
Normalizing factor for derivatives of Legendre polynomials      124Ч125
Normalizing factor for Hermite polynomials      177Ч178
Normalizing factor for Jacobi polynomials      171Ч172
Normalizing factor for Laguerre polynomials      185
Normalizing factor for Legendre polynomials      51Ч52
Odd function      7
Orthogonal polynomials      45Ч68 123Ч125 149Ч208 213Ч216 223Ч228
Orthogonality      3 224
Orthogonality, of Bessel functions      71Ч73 82Ч84
Orthogonality, of functions of two variables      117 122Ч124 140
Orthogonality, of Hermite polynomials      177 226
Orthogonality, of Jacobi polynomials      167Ч168
Orthogonality, of Laguerre polynomials      184Ч185 227
Orthogonality, of Legendre polynomials      50Ч51
Orthogonality, of sines and cosines      2Ч3
Orthonormal functions      152
Orthonormal polynomials      154
Parseval, M.A.      29 31 216
ParsevalТs theorem      29Ч31
Pearson, K.      142 147 162 165 230
Peebles, G.      203
Period      1
Po1ya, G.      230
Poisson, S.D.      103 105 136 137
PoissonТs integral      105 136Ч37
Polar coordinates      101Ч103
Probability integral      178
Recurrence formulas for Bessel functions      85Ч87 218
Recurrence formulas for general orthogonal polynomials      156Ч157
Recurrence formulas for Hermite polynomials      179Ч180
Recurrence formulas for Jacobi polynomials      172Ч173
Recurrence formulas for Laguerre polynomials      186Ч187
Recurrence formulas for Legendre polynomials      46Ч47 58Ч60
Recurrence formulas for sines and cosines      211Ч212 225
Riemann Ч Weber      230
Riemann, B.      14 16 21 25
RiemannТs theorem      14Ч16
Rietz, H.L.      230
Robertson, H.P.      230
Rodrigues, O.      57 166 167
RodriguesТs formula      57Ч58
Rolle, M.      78
Schmidt, E.      151 152 224 225
SchmidtТs process of orthogonalization      151Ч153
Schrbdinger equation      181Ч183 188Ч190
Schrodinger, E.      182 188
Schwarz, H.A.      38 39 195 202 204 207 215 224 228
SchwarzТs inequality      38 224
Shohat, J.      230
Sine series      7 8Ч10 94 95 98Ч99 100 101 112
Singular points of differential equations      70 88Ч89
Spherical coordinates      106Ч109 118Ч120 189
Spherical harmonics      118Ч138 189
Steinhaus, H.      229
Stone, M.H.      230
Sturm Ч Liouville boundary value problem      89Ч90
Sturm, C.      89
Summation of series      31Ч35
Szego, G.      174 205 230
Taylor, B.      78
Tchebichef, P.L.      150 230
Titchmarsh, E.C      230
Tonelli, L.      230
Transformation of LaplaceТs equation      101Ч103 105Ч107 129Ч131
Trigonometric sum      25Ч26
Ultraspherical polynomials      225Ч226
Uniform convergence      21Ч22 42Ч44 215
Uspensky, J.V.      230
Van der Waerden, B.L.      189 230
Vibrating membrane      112Ч114 221 222Ч223
Vibrating string      96Ч101 220Ч221
von Mises, R.      230
Walsh, J.L.      230
Watson, G.N.      230
Wave equation of hydrogen atom      188Ч190
Wave equation of linear oscillator      181Ч183
Weierstrass, K.      25 26 32 35 40 137 212 216 227
WeierstrassТs theorem for trigonometric approximation      25Ч27 35Ч40
Weight function      72 149Ч150 153Ч154
Weight function for Hermite polynomials      176
Weight function for Jacobi polynomials      166
Weight function for Laguerre polynomials      184
Weyl, H.      183 189 230
Whittaker, E.T.      230
Zeros of Bessel functions      72Ч73 76Ч79 82 87 218 219
Zeros of general orthogonal polynomials      159Ч160
Zeros of Legendre polynomials      52Ч53
Zygmund, A.      24 230
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