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In mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered and proved by Leonard James Rogers ( 1894 ), and were subsequently rediscovered (without a proof) by Srinivasa Ramanujan some time before 1913.
The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument.
Leonard James Rogers. Leonard James Rogers FRS [1] (30 March 1862 – 12 September 1933) was a British mathematician who was the first to discover the Rogers–Ramanujan identity and Hölder's inequality, and who introduced Rogers polynomials. [2] The Rogers–Szegő polynomials are named after him.
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In mathematics, the Rogers polynomials, also called Rogers–Askey–Ismail polynomials and continuous q-ultraspherical polynomials, are a family of orthogonal polynomials introduced by Rogers (1892, 1893, 1894) in the course of his work on the Rogers–Ramanujan identities.
Chopra says Rodgers was immediately “really trusting” with him and Hughes, adding that throughout their year working together on the documentary, Rodgers “was very open and vulnerable.”
Sylvie Corteel and Jeremy Lovejoy, Frobenius Partitions and the Combinatorics of Ramanujan's Summation Fine, Nathan J. (1988), Basic hypergeometric series and applications , Mathematical Surveys and Monographs, vol. 27, Providence, R.I.: American Mathematical Society , ISBN 978-0-8218-1524-3 , MR 0956465
Conditional trigonometric identity; Cyclotomic identity; D. ... Rogers–Ramanujan identities; S. Selberg's identity; List of set identities and relations; Sich ...