Author : Sonia Badesara

Early in 1920, three months before his death, Ramanujan wrote his last letter to Hardy. In the course of it he said: I discovered very interesting functions in recent times which I call ‘Mock θ- functions’. Unlike the ‘False θ-functions’, they enter into mathematics as wonderfully as the ordinary θ- functions. I am sending you with this letter some examples. The letter was accompanied by five foolscap passes. In the first three pages Ramanujan explained what he meant by a ‘Mock θ- function’. Hardy’s comment about Mock θ- function is; A Mock θ- function is a function defined by a q-series, convergent when |q|<1. We can calculate asymptotic formulae for it, when q tends to a rational point e 2πir/s of the unit circle of the same degree of precision these furnished for the ordinary θ- function by the theory of linear transformation.

Keywords: Hypergeometric functions, Mock Theta function

Article published in International Journal of Current  Engineering  and Technology, Vol.4,No.3 (June- 2014)