Simpler proofs were afterwards found by Prof. Rogers and myself.
I have now found an algebraic relation between and , viz.:
Another noteworthy formula is
Each of these formulæ is the simplest of a large class.
↑Proc. London Math. Soc., Ser. 1, Vol. xxv, 1894, pp. 318–343.
↑Proc. Camb. Phil. Soc., Vol. xix, 1919, pp. 211–216. A short account of the history of the theorems is given by Mr Hardy in a note attached to this paper. [For Ramanujan's proofs see No. 26 of this volume: those of Rogers, and the note by Hardy referred to, are reproduced in the notes on No. 26 in the Appendix.]
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