Irrational Behaviour of Bilateral Mock Theta Functions of Order Seven at Infinite Number of Points

Abstract

At the beginning of 1920, three months before his demise, Ramanujan addressed mock theta functions in his last letter to G. H. Hardy. He presented seventeen examples, and assigned them to orders three, five, and seven. Shukla and Ahmad obtained eight bilateral mock theta functions of order seven in 2003, and they proved that these functions satisfy the characteristic property of the mock theta function. In this paper it has been shown that four bilateral mock theta functions of order seven are irrational at q = ±½, ±⅓, ±¼, · · · , and four are irrational at q = ½, ⅓, ¼, · · · .