mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered...
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framework for the Rogers–Ramanujan identities and their arithmetic properties, solving a long-standing mystery stemming from the work of Ramanujan. The findings...
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independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of...
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advanced results. During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel;...
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James Rogers in 1894, and then independently by Ramanujan in 1913 and Schur in 1917, in what are now known as the Rogers-Ramanujan identities. It states...
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Leonard James Rogers FRS (30 March 1862 – 12 September 1933) was a British mathematician who was the first to discover the Rogers–Ramanujan identity and Hölder's...
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orthogonal polynomials introduced by Rogers (1892, 1893, 1894) in the course of his work on the Rogers–Ramanujan identities. They are q-analogs of ultraspherical...
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hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan identities. Slater was born in 1922 and homeschooled for much of her early...
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algebras. Howard Garland and James Lepowsky demonstrated that Rogers–Ramanujan identities can be derived in a similar fashion. The initial construction...
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Bailey pair (redirect from Slater's identities)
Bailey (1947, 1948) while studying the second proof Rogers 1917 of the Rogers–Ramanujan identities, and Bailey chains were introduced by Andrews (1984)...
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function is absolutely convergent. Dixon's identity Rogers–Ramanujan identities Bressoud, D. M. (1981), "Some identities for terminating q-series", Mathematical...
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Q-Pochhammer symbol (section Identities)
theorem q-derivative q-theta function q-Vandermonde identity Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Berndt, B. C. "What is a q-series...
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notebook Ramanujan's master theorem Ramanujan's sum Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Ramanujan–Sato series Ramanujan magic...
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students. Gordon is well known for Göllnitz–Gordon identities, generalizing the Rogers–Ramanujan identities. He also posed the still-unsolved Gaussian moat...
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Chihara–Ismail polynomials. Ismail also worked on q-series and Rogers–Ramanujan identities. Ismail is also interested in the combinatorial theory of orthogonal...
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mathematical work in nonlinear differential equations and the theory of Rogers-Ramanujan identities". His doctoral students include Rinat Kedem, Anne Schilling,...
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Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year...
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solved by Baxter (1980), who found that it was related to the Rogers–Ramanujan identities. The hard hexagon model occurs within the framework of the grand...
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Jacobi triple product (redirect from Jacobi triple product identity)
_{n=-\infty }^{\infty }(-1)^{n}q^{\frac {3n^{2}-n}{2}}.} The Rogers–Ramanujan identities follow with x = q 2 q {\displaystyle x=q^{2}{\sqrt {q}}} , y...
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Landau–Ramanujan constant, Ramanujan–Soldner constant, Ramanujan–Petersson conjecture, Rogers–Ramanujan identities, Hardy–Ramanujan number. John Rambo, American...
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(1922–2008), British expert on hypergeometric functions and the Rogers–Ramanujan identities Angela Slavova, Bulgarian expert on waves and cellular neural...
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Ramanujan's sum, Rogers–Ramanujan identities, Ramanujan's master theorem: Discovered by the Indian mathematician, Srinivasa Ramanujan. Chandrasekhar limit...
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numbers (see also the first item of the section Analysis). The Rogers–Ramanujan identities are proved using Markov chains. A non-probabilistic proof was...
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Rodrigues: Rodrigues formula Leonard James Rogers: Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegő polynomials Schubert polynomial...
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Bailey, W. N. (1951), "On the simplification of some identities of the Rogers-Ramanujan type", Proceedings of the London Mathematical Society, Third...
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Square root of 5 (section Identities of Ramanujan)
appears in various identities discovered by Srinivasa Ramanujan involving continued fractions. For example, this case of the Rogers–Ramanujan continued fraction:...
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number theory, finding deep generalizations and analogs of the Rogers–Ramanujan identities. Ron Cohen Anton Kapustin Ernest Baver Boris Gotkin Umut Gursoy...
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Mock modular form (category Srinivasa Ramanujan)
others, who proved Ramanujan's statements about them and found several more examples and identities. (Most of the "new" identities and examples were already...
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Brenner, Charles H. (November 1986). "Asymptotic Analogs of the Rogers-Ramanujan Identities in Number Theory". Journal of Combinatorial Theory, Series A...
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}{3}}\right)-1}}.} Berndt, B. et al. "The Rogers–Ramanujan Continued Fraction" Berndt, Bruce C. (1998). Ramanujan's Notebooks Part V. Springer. ISBN 978-1-4612-7221-2...
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