Algebraic relations between certain infinite products
It was proved by Prof. L. J. Rogers that
Simpler proofs were afterwards found by Prof. Rogers and myself.I have now found an algebraic relation between and , viz.:
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.]