# theta functions

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Related to theta functions: Theta series

## theta functions

[′thād·ə ‚fəŋk·shənz]
(mathematics)
Complex functions used in the study of Riemann surfaces and of elliptic functions and elliptic integrals; they are: where q = exp π i τ, and τ is a constant complex number with positive imaginary part.
References in periodicals archive ?
The theta function of a characteristic m of degree g is the series
Ramanujan's general theta function f(a, b) is defined by
With respect to the (quasi) period [pi] and [pi][tau], Jacobi theta functions [[theta].
In the letter, Ramanujan defined four third order mock theta functions, ten fifth order mock theta functions and three seventh order mock theta functions.
Key words: Jacobian theta functions, especially products; normalizing factors.
The two subjects, elliptic functions and theta functions, developed in the nineteenth century, are intimately connected with each other.
Gordon and McIntosh  gave a method of constructing mock theta functions by performing left-shift transformation on certain q-series.
Since that time, the mock theta functions have cropped up in a surprising array of fields, including number theory, probability' theory, and statistical mechanics.
This information is obtained with the help of a relation that generalises the reciprocity law for Jacobi's theta functions (see Lemma 2).
SAFE, Convergence of Pade approximants of partial theta functions and the Rogers-Szego polynomials, Constr.
His topics include the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, the Rogers-Fine identity, Bailey chains, WP-Bailey pairs and chains, further results on Bailey/WP-Bailey pairs and chains, bijective proofs of basic hypergeometric identities, q-continued fractions, Lambert series, and mock theta functions.
The half-shift transformation was introduced by Gordon and McIntosh (6) to develop eighth order mock theta functions.

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