- 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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