Irrational Behavior of Bilateral Mock Theta Functions

Abstract

Ramanujan was the first who introduced the mock theta functions in his last letter to G. H. Hardy in January 1920. Shukla and Ahmad obtained bilateral mock theta functions of order 7, 9, …, 2r + 1, and they have shown that these functions meet the mock theta function’s distinctive attribute. This article shows the irrational behavior of bilateral mock theta functions of order 2r + 1 at the points q = ±1/2, ±1/3, ±1/4, …. Based on this behavior, irrational behavior of bilateral mock theta functions of order 5, 7, 9, … has also been discussed.