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A brief introduction to theta functions

Author: Richard Bellman
Publisher: New York : Holt, Rinehart and Winston, 1961.
Series: Athena series.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Bellman, Richard, 1920-1984.
Brief introduction to theta functions.
New York, Holt, Rinehart and Winston [1961]
(OCoLC)655000813
Document Type: Book
All Authors / Contributors: Richard Bellman
OCLC Number: 426806
Description: x, 78 pages ; 25 cm.
Contents: 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 [theta]₃(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 [theta]₄ʹ(z)/[theta]₄(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 [integral][lemniscate] e⁻([superscript y, Ty]) dy --
The modular transformation --
Generalizations and particularizations.
Series Title: Athena series.
Responsibility: Richard Bellman.

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