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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.
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.
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.
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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
Dougall–Ramanujan [1] Landau–Ramanujan constant; Ramanujan's congruences; Hardy–Ramanujan number; Hardy–Ramanujan theorem; Hardy–Ramanujan asymptotic formula; Ramanujan identity; Ramanujan machine; Ramanujan–Nagell equation; Ramanujan–Peterssen conjecture; Ramanujan–Soldner constant; Ramanujan summation; Ramanujan theta function ...
Identity management (ID management) – or identity and access management (IAM) – is the organizational and technical processes for first registering and authorizing access rights in the configuration phase, and then in the operation phase for identifying, authenticating and controlling individuals or groups of people to have access to applications, systems or networks based on previously ...
Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the ...