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| Bellman R. — A brief introduction to theta functions |
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| Предметный указатель |
Abel 8
Analytic paraphrase 20
Approximate functional equation 53
Approximations 11
Arithmetic-geometric mean 55
Automorphic functions 13—15
Bailey, W.N. 48
Baker, H.F. 58 70
Barrucand, P. 29
Basic hypergeometric series 47—49
Basoco, M.A. 52
Bell, E.T. 54
Bellman, R. 23 51 58 62 65 68 70 71 72
Bessel function 23 26—27
Binomial expansion 40—41
Bochner, S. 21 25 29 68
Cauchy 58
Circle method 14—15
Cyclotomic sums 40
De La Vallee Poussin 33
Dickson, L.E. 4
Diffusion 41
Diffusion equation 13
Dirichlet divisor function 37
Dirichlet divisor problem 23
Dirichlet series 28 36—37
Doetsch, G. 18 21 23 26 27 29
Dragonette, L.A. 52
Duplication formula 30
Eisenstein 12 13 15 23
Eisenstein series 12 71
Erdelyi, A. 27
Estermann, T. 58
Euler 1 5 8 33 42 47 49 50
Euler factorization 33
Eulerian results 47—48
Fake theta functions 52
Fejer, L. 6 18
Ferrar, W.L. 34 36 37
Formulae duplication 30
Formulae inversion 28
Formulae Poisson summation 6—7 9 34 36 67
Formulae summation 36 37
Formulae transformation 10—11
Forsyth, A.R. 58 70
Fourier expansion 45
Fourier series 4—7
Fuchs 15
Fueter, R. 15
Functional equation 32 33 39
Functions, automorphic 13—15
Functions, Bessel 23 26—27
Functions, Dirichlet divisor 37
Functions, fake theta 52
Functions, gamma 30
Functions, Gauss circle 37
Functions, mock theta 48 51—52
Functions, modular 12 68 71
Functions, multidimensional theta 64 70 72
Functions, Riemann Zeta 30—32
Functions, theta 1—3
Functions, zeta 34—36
Fundamental domain 3—4
Gamma function 30
Gauss circle function 37
Gauss sum 38 50 52
Gauss, C.F. 1 30 37 38 39 49 55
Gotzky, F. 71
Gronwall 33
hadamard 33
Hamburger, H. 21 24
Hardy, G.H. 14 15 16 33 48 49 50 53
Heat equation 16
Hecke, E. 7 8 15 23 25 71 72
Heine, E. 48
Hermite, C 45 47 48 60
hilbert 34 71
Hypergeometric series 48
Infinite integral 68 69
| Infinite product 43 51 62
Ingham 33
Integral identities 69
Inversion formula 28
Jacobi, C.G. 1 48 53 54 58 64
Kloosterman, H.D. 71
Kober, H. 27
Kochliakov, S. 37
Kronecker, L. 52 53
lame 48
Landau, E. 33 72
Landen 55
Landen transformation 55
Landsberg, M. 39 40
Laplace transform 20
Lattice points 16
legendre 30
Lehman, S. 62
Lemniscate 40
Lenz, H. 42
Lerch, M. 21 40 52
Lindelof, E. 8 40
Linfoot, E.H. 9
Liouville 1
Liouville’s theorem 1 44 46
Littlewood 14 33 53
Maass, H. 20 71 72
McMahon, P.A. 49
mellin 29—30
Mellin transform 28—31
Michelangelo 48
Mock theta functions 48 51—52
Modular functions 12 68 71
Modular transformation 70 71
Mordell integral 52—53
Mordell, L.J. 3 9 23 36 40 47 48 52 53 68 71
Multidimensional Fourier series 66
Multidimensional Poisson summation formula 67
Multidimensional theta functions 64 70 72
Olkin, I. 70
Partial fractions 50—51
Perron, O. 49
Plana 8
Poincare 58
poisson 4 8
Poisson summation formula 6—7 9 34 36 67 68
Ramanujan 14 15 21 47 48 51 52
Random walk 41
Riemann hypothesis 33—34
Riemann zeta function 30—32
Riemann, B. 30 32 33 52 53 58
Rogers, L.J. 52
Schaar 39
Schlesinger, L. 15
Schoeneberg, B. 25
Schottky, F. 56 57
Selberg 33
Shanks 50
Siegel, C. L. 20 52 68 71
Similarity solution 19
Sklar, A. 38
Spherical harmonics 25
Stirling 40
Summability theorem 5—6
Summation formulae 36 37
Superposition 17
Theta function 1—3
Titchmarsh, E. C 7 9 16 21 29 33 34 53
Transformation formula 10—11
van der Corput 52
van der Pol 54 57
voronoi 23 37
Watson, G. N. 2 4 8 12 20 30 42 44 46 47 48 52 53 54 55
Weber 3
Whittaker, E. T. 2 4 12 20 30 42 44 47 53 54 55
Widder, D. V. 21
Wright, E. M. 16 49 50
Zeroes 42—43
Zeta function 34—36
Zygmund, A. 7
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