Asymptotics for Bailey-type mock theta functions

We compute asymptotic estimates for the Fourier coefficients of two mock theta functions, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ the circle method due to Wright and a modified Tauberian theorem. We encounter cancelation in our estimates for one of the mock theta functions due to the auxiliary function $$\theta _{n,p}$$ θ n , p arising from the splitting of Hickerson and Mortenson. We deal with this by using higher-order asymptotic expansions for the Jacobi theta functions.

Some new transformation formulas deriving from Bailey pairs and WP-Bailey pairs

The purpose of this paper is to derive a new Bailey pair and three new WP-Bailey pairs from four summation formulas of the multibasic hypergeometric series. As applications, we will use them to obtain many new transformation formulas for basic and multibasic hypergeometric series.

A note on Bailey and WP-Bailey Pairs

In this paper, we have established certain theorems involving Bailey pairs and WP-Bailey pairs. Further, making use of some known WP-Bailey pairs and theorems for constructing new WP-Bailey pairs, we have also established transformation formulas for q-hypergeometric series.

Some further Hecke-type identities

In this paper, we obtain some Hecke-type identities by using two [Formula: see text]-series expansion formulae. And, the identities can also be proved directly in terms of Bailey pairs. In particular, we show that certain partial theta functions and the theta functions can be expressed in terms of Hecke-type identities.

Certain applications of WP-Bailey pairs

In the present paper, certain new transformation formulae for basic hypergeometric series have been developed with the help of new WP-Bailey pair generated from old WP-Bailey pair.