Algebraic relations between certain infinite products

Algebraic relations between certain infinite products
by Srinivasa Ramanujan
123600Algebraic relations between certain infinite productsSrinivasa Ramanujan

It was proved by Prof. L. J. Rogers[1] that

and

Simpler proofs were afterwards found by Prof. Rogers and myself[2].

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.


  1. Proc. London Math. Soc., Ser. 1, Vol. xxv, 1894, pp. 318–343.
  2. 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.]

This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.

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