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| Grosswald E. — Bessel Polynomials |
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| Предметный указатель |
Abdi, W.H. F 150 164
Abramovitz, M. F 171
Agarwal, R.P. F 2 149 151 164
Al-Salam, W.A. F 2 43 44 73 149 151 154 158—160 164
Arithmetic properties of BP 155
Askey, R. 158 171
Asymptotic properties, or relations 2 4 82 93 124—130 163
Asymptotic series 124 163
Baicev, I. 155 164
Bailey, W.N. 171
Banerjee, D.P. 155 164
Barnes, C.W. 3 164
Bendixson — Hirsch theorem 3 90 91
Bendixson, I. 3 90 171
Berlekamp, E.R. 121
Bernoulli numbers 154
Bernstein, S. I 137
Bernstein’s Theorem I 137 138
Bertrand’s postulate 102
Bessel alternative (orthogonality) 26 162
Boas, R.P. Jr. 2 8 64 65 67 162 164 171
Bochner, S. 1 164
Bondesson, L. 136 171
Borel transform see “Laplace transform”
Borel, E. 66
Boudra, P.W. Jr. 167
Brafman, F. 2 45 46 149 153 164
Breusch, R. 102 171
Brillhart, J.D. 121
Brown, J.W. 164
Buck, R.C. 2 8 64 65 67 162 164 171
Burchnall, J.L. 1 2 6 10 15 42 43 49 51 65 70 76 93 94 143 149 156 164
Burnside, W. 117 171
Cardioid 88
Carlitz, L. 2 45 57 73 74 154—156 160 164 165
Carlson, B.C. 165
Cartwright, M.L. 171
Cauchy product 45
Cauchy, A.L. 117
Center of mass 83 84
Characteristic (eigen-) values 88—91
Characteristic functions 136
Chatterjea, S.K. 46 49 154 155 157 165 166
Chatterjee, C.K. 156 166
Chaundy, T.W. 1 2 6 10 164
Chen, M.P. 49 166
Chihara, T.S. 154 164
Christoffel constants 147 149
Christoffel — Darboux (type) identitios 154 156
Cima, J.A. 155 157 166
Commutation relations 47 48
Continued fractions 3 34 59—63 81 160
Convergence 64 65 66 68 69 72 74 155 157 160 162
Cramer’s Rule 20
CYCLE 117
Das, M.K. 46 157 166
Davenport, H. 171
Dedeking, R. 117
Delay flat 145
Delay maximally flat 2 145
Delay phase 144
Delay time 141 142 143
Dhawan, G.K. 166
Dickinson, D. 2 38 46 73 81 157 160 166
Differential equations of  158
Differential equations of  -form 9—12 14—15 35
Differential equations of BP I 1 4—17 36 38 85
Differential equations of Sturn — Liouville form 49
Differential, difference relations 159
Discriminant 116 118 119
Distortion factor 143
Docev, K. 2 13 81 86 124 125 128 130 157 159 162 166
Doetsch, G. 171
du Plessis, N. 39 173
Dumas, M.G. 100 171
Dutta, M. 157 166
Eigenvalues see “Characteristic values”
Eisenstein, F.M.G. 102
Eisenstein’s criterion (irreducibility) 102
Elements (of Newton polygons) 107 109
Enestroem 77 171
Erdelyi, A. 166
Euler, L. 171
Eweida, M.T. 157 166
Expansion formulae 151—153 160
Expansions in series of BP I 46 64—74 157 159 160 162
Expansions in series of other functions 11 47 91
Feldheim, E. 43 171
Feller, W. 171
Feng, C.C. 49 166
Filter 141 143 144
Ford, L.R. 171
Fourier analysis 133
Fourier transforms 26 136
frequency I 133 136 140 141 144
Frink, O. F I 1 2 7 12 24 44 64 145 149 152 158 162 167
Frobenius’ method 5 12
Functions Associate Legendre 134 135
Functions Bessel 2 3 4 19 35 38 47 91 152 157 158
Functions Bessel, modified 4 5 18 19 34 76 91 92 137 144 158
Functions beta 36 38 132
Functions exponential I 3 67 68 73 74 125 131
Functions exponential type 67 69 72
Functions greatest integer I 97 98 102 132
Functions Hankel 91 92
Functions Hankel, modified I (see also “Bessel modified”)
Functions hypergeometric 2 34 38 150
Functions hypergeometric, generalized 34
Functions Lebesgue integrable 136
Functions MacDonald see “Bessel or modified”
Functions Meijer’s G 157
Functions positive real (p.r.) 141 142
Functions step 154
Functions Whittaker 34 37 38 153
Gauss — Lucas Theorem 84
Generating functions 1 2 36 41—50 57 58 67 70 150 151 153 160 162
Generating functions, bilinear 44
Gershgorin, S. 3 88 90
Gershgorin’s theorem 3 88 90 91
Gnedenko, B.V. I 171
Gould, H.W. F 57 171 172
Gram-Schmidt method 25
Grosswald, E. I 2 3 39 121 166 167 172
Grosswald, V. F
Group alternating 116—118 120 122
Group Galois I 2 116—123 163
Group primitive 116—118 120—122
Group symmetric 116 118 120—122 163
Group transitive 116—118 120 121
Guillemin, E. 3 167
Hahn, W. 1 167
Hamburger, H. 25 172
Hamza, A.M. 158 167
Hazony, D. 3 167
Hensel, K. 172
Hermite, C. I 1 26 172
Hermitian matrices 90
Herstein, I.N. 39 172
Hille, E. 172
Hirsch, M.A. 3 90 172
Hurwitz, A. 77 78 141 142 143 172
Impedance (driving point, complex) 2 141 142
Indicial equation 5
Infinite divisibility I 3 136—139
Inner product 25 26
Inverse transform see “Laplace transform”
Inversion formula 66
Irrationality of  (r rational) I 125—131
Irrationality of  I 131—133
Irreducibility 2 99—117 120 121 123 154 163
| Ismail, M.E.H F I 3 137 158 167 172
Iversen, K.E. 172
Jackson, D. 172
Jayne, J.W. 26 167
Johnson, D.E. 167
Johnson, J.R. 167
Jordan, C. 117 172
Kakeya, S. 77 172
Karlin, S. 155
Kelker, D.N. I 3 136 137 158 167
Kloss, K. 121
Kolmogorov, A.N. I 171
Krall, A.M. F 26 167 168
Krall, H.L. F I 1 2 7 12 24 44 64 145 149 152 158 162 167 172
Kronecker delta I 26 32 146 154
Krylov, V.I. 149 167
Kublanowskaya, V.N. 149 167
Lagrange interpolation 146
Laguerre, E. 26 82 83 84 172
Laguerre’s Theorem 82 83 84
Lambert, J.H. 59 173
Landau, E. 173
Landsberg, O. 172
Laplace (or Borel) transform and inverse transform I 66 67 69 137 138 140—142 144—149
Laplace, P.S. I
Laplacian see “Operators Laplacian”
Lebesgue constants 162
Legendre, A.M. I 103
Legendre’s equation I 134
Leibniz’s Rule 16 29 53 55 132
Lemniscate 70 71
Levy, P. I 173
Lie algebra 48
Lie group 41 46 47
Lindeloef, E. 66
Luke, Y.L. 149 167
Magnus, W. 166
Marcus, M. 173
McBride, E.B. 46 167
McCarthy, P. 2 81 159 168
Measure 137
Miller, W. Jr. 170
Mine, H. 173
Mittal, H.B. 168
Moments 25—32 51 53
Monotonicity, monotonic I 68 75 78 80
Monotonity, complete I 3 136—139
Moore, M.L. 157 166
Morton, R.D. 26 168
Multiplication theorems 153
Nasif, M. 2 65 81 168
Networks, electrical 2 3 139—145
Networks, passive 141 142
Networks, R-L-C 143
Networks, “Bessel” case 142
Newman, M. 121
Newton identities (coefficients, zeros) 93 94 97 98
Newton polygon 100—115
Oberhettinger, F. 166
Obreshkov, N. 13 124 157 159 168
Ohm — Kirchhoff laws, equations 139—141
Olds, C.D. 1 168
Olver, F.W.J. 2 91 92 93 162 168 173
Operational formulae 155 157 160
Operators difference 152 156
Operators differential I 9—12 14 15 35 46 47 51 133 155—157 160
Operators Laplacian I 133
Operators other 159 160
Operators shift 48 49
Orthogonality I 25—32 64 135 154 155 158 160 orthogonal”
Orthonormality 26
Pade table and approximants 3 160
Paliwal, D.D. 166
Parodi, M. 3 88 89 90 162 168
Permutation 117 121
Perron, O. 173
Pham-Ngoc Dinh, A. 159 168
Phragmen, E. 66
Piessens, R. 149 168
Polar axis I 133
Pole (of center of mass) 83 84
Polynomials Appell (classical, or generalized) 65—68
Polynomials associate BP 153
Polynomials basic BP 151
Polynomials generalized BP 12—17 22—24 27 29—32 35—38 42—45 49—51 54 55 64 65 70 75 80—82 85—88 93 94 125 128—130 148 149 151—163
Polynomials Hermite 26 45 154
Polynomials Hurwitz 141—143
Polynomials Jacobi 26 34 35 38 43 151 154 160
Polynomials Laguerre 26 34 36 38 44 152 154 155 160
Polynomials Legendre I 39 134 135 145 160
Polynomials Lommel 34 38 46 81
Polynomials monic 99 103 118 119 123
Polynomials orthogonal, classical 3 26 34 47 64 154 162
Polynomials orthogonal, other 153 157—160
Polynomials reverse BP 7 8 12
Polynomials totally positive 160
Probability distribution, density function 136
Pseudogenerating functions of BP 1 42
Quadrature, formulae 146 148
Quadrature, Gaussian 145 147
Ragab, F.M. 2 149 159 168
Rainville, E.D. 2 39 43 151 168 173
Rajagopal, A.K. 160 168
Random variable 136
Recurrence relations 1 2 9 18—24 36 59 60 86 87 94 96 143 151—153 155 158 162
Relations of BP to other functions 2 34—40 154 155 157 158
Representation formulae of BP by determinants 3 20—22 88 155
Representation formulae of BP by integrals 151 156 157 160 161
Representation formulae of BP by other functions 35—38 155
Representation formulae of other functions by BP 46
Representation formulae others 45 46 151 153 155
Resultant 118 119
Rodrigues (type) formulae 16 36 51—58
Romanovsky, V. 1 168
Rusev, P. 160 169
Rutishauser, H. 160 169
Saff, E.B. 2 86 162 169
Salzer, H.E. 145 149 169
Scheme of factorization 109—111 113 115
Scheme of factorization, compatibility or incompatibility 109 110 112 115
Schmidt method see “Gram — Schmidt method”
Schur, I. 39 102 116 117 173
Segun, I.E. F 171
Separation of variables I 133 134
Shepard, R.R. 3 169
Siegel, C.L. I 131 173
Singularities, singular points 4 69 148
Sizemore-Ballard, G. F
Skoblja, N. 149 167 169
Smirnova, T.N. 149 167
Soni, S.L. 160 169
Special functions 3
Spots 100 104—109 111
Srivastava, H.M. 160 169
Stauduhar, R. 121
Stieltjes, T.J. 25 173
Stirling formula I 124 125 127 129 131 132
Stirling numbers 9
Stokes, V.P. 167
Storch, L. 3 144 169
Stratton, J.A. 173
Student t-distribution I 136—139
Summability 64—66 69 72 74 155 162
Synthesis (of a network) 3 140
Szegoe, G. 82 173
Szegoe, P. 155
Tchebycheff, P.L. 25 102 173
Thomson, W.E. 2 3 143 169 170
Thorin, O. 136 173
Toscano, L. 2 3 160 170
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