Cubic analogues of the Jacobian theta function θ(z,q)

Title: Cubic analogues of the Jacobian theta function θ(z,q)
Creator: Hirschhorn, Michael; Garvan, Frank; Borwein, Jon
Relation: Canadian Journal of Mathematics Vol. 45, Issue 4, p. 673-694
Publisher Link: http://dx.doi.org/10.4153/CJM-1993-038-2
Publisher: University of Toronto Press
Resource Type: journal article
Date: 1993
Description: There are three modular forms a(q), b(q), c(q) involved in the parametrization of the hypergeometric function ₂F₁( 1/3, ^2/3 ₁,) analogous to the classical θ₂(q),θ₃(q),θ₄(q) and the hypergeometric function ₂F₁(1/2,^1/2 ₁,)• 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.
Subject: Jacobian theta function; hypergeometric function; Jacobi triple product identity
Identifier: http://hdl.handle.net/1959.13/940977
Identifier: uon:13148
Identifier: ISSN:0008-414X
Language: eng
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