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Cubic Analogues of the Jacobian Theta Function θ(z, q)

Published online by Cambridge University Press:  20 November 2018

Michael Hirschhorn ,
Frank Garvan  and
Jon Borwein
Michael Hirschhorn
Affiliation:
School of Mathematics, University of New South Wales, PO Box 1, Kensington, NSW 2033, Australia
Frank Garvan
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, B3H 3J5
Jon Borwein
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1
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Abstract

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There are three modular forms a(q), b(q), c(q) involved in the parametrization of the hypergeometric function analogous to the classical θ2(q), θ3(q), θ4(q) and the hypergeometric function We give elliptic function generalizations of a(q), b(q), c(q) analogous to the classical theta-function θ(z, q). A number of identities are proved. The proofs are self-contained, relying on nothing more than the Jacobi triple product identity

Keywords

33D1005A1911B6511F2733C05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 673 - 694
Copyright
Copyright © Canadian Mathematical Society 1993

References

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