Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Introduction . 1 1 The Heine Transformation . 1 Introduction . 2 Heine’s Method . 3 Ramanujan’s Proof of the q-Gauss Summation Theorem . 5) . 7) . 10) . 2 and Auxiliary Results . 27 2 The Sears–Thomae Transformation . 1 Introduction . 3) . 3) .