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I've been really trying to prove Ramanujan Partition theory, and different sources give me different explanations. Can someone please explain how Ramanujan (and Euler) found out the following equation for the number of partitions for a given integer? Any help is appreciated thank you so much!

$$P(n)\sim\frac1{4n\sqrt3}\exp(\pi\sqrt{2n/3})$$ enter image description here

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There is a proof in Ramanujan: Twelve Lectures by Hardy.

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Another reference is Atle Selberg's paper "Reflections around the Ramanujan centenary". More precisely, the appendix, if I remember. It appears in the book "Ramanujan: essays and surveys". My recommendation would be to read that before Hardy, for reasons that Selberg himself explains.

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  • $\begingroup$ It seems that the paper is also in Selberg's Collected papers Vol. 1. (At least according to this.) $\endgroup$ – Martin Sleziak Jan 11 '17 at 12:00
  • $\begingroup$ Thank you so much. I will try to get hold of the book. Are there any online papers or links that would be helpful? My paper is due day after tomorrow, and purchasing a book might take a while. Thank you so so much. $\endgroup$ – Joseph Jan 11 '17 at 16:12

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