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MAT. IMPRESO
Autor Bellman, Richard

Título A brief introduction to theta functions / Richard Bellman

Publicación New York : Holt, Rinehart and Winston, 1961
Ubicación Signatura Tipo de préstamo Estado Notas
 B. Ciencias. Física/Química-Depósito  FQ-GAE 20    PRÉSTAMO LARGO  DISPONIBLE  Donación "Biblioteca Federico Gaeta Maurelo"
 Ciencias.Matemáticas-Dpto. Matemáticas. Análisis Matemático  M-ANALISIS    CONSULTAR DEPT  DISPONIBLE
Descripción física X, 78 p. : il. ; 24 cm
Colección Athena series
Athena series. Selected topics in mathematics
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Bibliografía p. 71-72. -- Índices p. 75-78
Contiene: Introduction -- The four types of theta functions -- Fundamental domain -- First basic result -- Fourier series -- The Poisson summation formula -- Some simple sufficient conditions -- An infinite integral -- The transformation formula for Θ₃(z, t) -- Numerical application -- Modular functions and Eisenstein series -- The constant c -- The heat equation -- Formal derivation of theorem 1 -- The Laplace transform -- Another infinite integral -- The transformed transformation formula -- Infinite products and by-products -- The general theta function transformation -- Some results of Doetsch -- Results of Kober-Erdelyi -- The Mellin transform -- An application of the Mellin transform -- The Riemann Zeta function -- An alternate form of he functional equation -- The Riemann hypothesis -- The Poisson summation formula and the zeta function -- A more general case -- Gaussian sums -- Polya's derivation -- Discussion -- A fundamental infinite product -- Zeroes -- Proof of theorem 6 -- An infinite series for Θ'₄(z)/Θ₄(z) -- A more interesting series -- Hermite's derivation -- Some results of Watson -- Eulerian results -- Euler's formulas and functional equations -- Partial fractions -- Mock theta functions -- The Mordell integral -- Some new types of relations -- Relations connecting squares of theta functions -- Additional formulae -- Landen's formula -- The fundamental transformation formula -- Some results of Schottky -- Functional equations -- Determination of theta functions -- Entire solutions -- Hermite's method -- Statement of result -- Fundamental transformation formula -- Determination of g(t) -- The infinite product -- LInear space of solutions -- Relations connecting squares -- Addition formula -- Multidimensional theta functions -- Vector-matrix notation -- Convergence proof -- Elementary functional relations -- Multidimensional Fourier series -- Multidimensional Poisson summation formula -- An infinite integral -- Evaluation of ∫[superscript (∝)] e[superscript -(y, Ty)] dy -- The modular transformation -- Generalizations and particularizations
Materia Funciones Theta
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