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 [5] 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.