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T. MacRobert (1955)
Higher Transcendental FunctionsNature, 175
S.M. Artem’eva, H.-W. Burmann (2004)
On the Relation Between Hypergeometric Functions and Some Multivalued FunctionsDiffer. Uravn., 40
V.V. Golubev (1950)
Lektsii po analiticheskoi teorii differentsial’nykh uravnenii (Lectures on the Analytic Theory of Differential Equations)
T. Apostol (1976)
Modular Functions and Dirichlet Series in Number Theory
Bateman Manuscript, H. Bateman, A. Erdélyi (1954)
Higher Transcendental Functions
A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi (1953)
Higher Transcendental Functions (Bateman Manuscript Project)
E. Hecke (1927)
Zur Theorie der elliptischen ModulfunktionenMathematische Annalen, 97
We study the relationship between two Hecke theta series, the Dedekind function, and the Gauss hypergeometric function. The main result of the present paper is given by formulas for the representation of the theta series in the form of compositions of the squared Dedekind function, a power of the absolute invariant, and canonical integrals of the second-order hypergeometric differential equation with special values of the three parameters. The proofs of these representations are based on the properties of the matrix transforming the canonical integrals of the Gauss equation in a neighborhood of zero into canonical integrals of the same equation in a neighborhood of unity.
Differential Equations – Springer Journals
Published: Mar 31, 2009
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