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• catalog contributor b2912152.
• catalog created "[1961]".
• catalog date "1961".
• catalog date "[1961]".
• catalog dateCopyrighted "[1961]".
• catalog description "An infinite integral -- Evaluation of [integral][lemniscate] e⁻([superscript y, Ty]) dy -- The modular transformation -- Generalizations and particularizations.".
• catalog description "Includes bibliography.".
• catalog description "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 -- ".
• catalog description "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 -- ".
• catalog extent "78 p.".
• catalog hasFormat "Brief introduction to theta functions.".
• catalog isFormatOf "Brief introduction to theta functions.".
• catalog isPartOf "Athena series; selected topics in mathematics".
• catalog issued "1961".
• catalog issued "[1961]".
• catalog language "eng".
• catalog publisher "New York, Holt, Rinehart and Winston".
• catalog relation "Brief introduction to theta functions.".
• catalog subject "517.36".
• catalog subject "Functions, Theta.".
• catalog subject "QA345 .B4".
• catalog tableOfContents "An infinite integral -- Evaluation of [integral][lemniscate] e⁻([superscript y, Ty]) dy -- The modular transformation -- Generalizations and particularizations.".
• catalog tableOfContents "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 -- ".
• catalog tableOfContents "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 -- ".
• catalog title "A brief introduction to theta functions.".
• catalog type "text".