Ramanujan R and S

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With (Mathematica's QPochhammer[a,q]), the expressions and represent Roger–Ramanujan and Roger–Ramanujan , also representable as and , using Mathematica's notation for continued fractions (the ContinuedFractionK[] function). In 1919, months before his death, Ramanujan wrote down various elegant results for this function in what became the "lost notebook."

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Ramanujan claimed that many equations like can be expressed in terms of radicals [1]. This notebook collects many of these results.

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Contributed by: Oleg Marichev, Michael Trott, and Ed Pegg Jr (April 2013)
Open content licensed under CC BY-NC-SA


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References

[1] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, New Delhi: Narosa Publishing House, 1988 p. 210.

[2] G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook: Part I, New York: Springer, 2005 pp. 58–84.

[3] Wikipedia. "Ramanujan's Lost Notebook." (Apr 9, 2013) en.wikipedia.org/wiki/Ramanujan%27s_lost _notebook.



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