mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered...

framework for the Rogers–Ramanujan identities and their arithmetic properties, solving a long-standing mystery stemming from the work of Ramanujan. The findings...

independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of...

advanced results. During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel;...

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...

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...

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...

hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan identities. Slater was born in 1922 and homeschooled for much of her early...

algebras. Howard Garland and James Lepowsky demonstrated that Rogers–Ramanujan identities can be derived in a similar fashion. The initial construction...

Bailey (1947, 1948) while studying the second proof Rogers 1917 of the Rogers–Ramanujan identities, and Bailey chains were introduced by Andrews (1984)...

function is absolutely convergent. Dixon's identity Rogers–Ramanujan identities Bressoud, D. M. (1981), "Some identities for terminating q-series", Mathematical...

theorem q-derivative q-theta function q-Vandermonde identity Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Berndt, B. C. "What is a q-series...

notebook Ramanujan's master theorem Ramanujan's sum Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Ramanujan–Sato series Ramanujan magic...

students. Gordon is well known for Göllnitz–Gordon identities, generalizing the Rogers–Ramanujan identities. He also posed the still-unsolved Gaussian moat...

Chihara–Ismail polynomials. Ismail also worked on q-series and Rogers–Ramanujan identities. Ismail is also interested in the combinatorial theory of orthogonal...

mathematical work in nonlinear differential equations and the theory of Rogers-Ramanujan identities". His doctoral students include Rinat Kedem, Anne Schilling,...

Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year...

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...

_{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...

Landau–Ramanujan constant, Ramanujan–Soldner constant, Ramanujan–Petersson conjecture, Rogers–Ramanujan identities, Hardy–Ramanujan number. John Rambo, American...

(1922–2008), British expert on hypergeometric functions and the Rogers–Ramanujan identities Angela Slavova, Bulgarian expert on waves and cellular neural...

Ramanujan's sum, Rogers–Ramanujan identities, Ramanujan's master theorem: Discovered by the Indian mathematician, Srinivasa Ramanujan. Chandrasekhar limit...

numbers (see also the first item of the section Analysis). The Rogers–Ramanujan identities are proved using Markov chains. A non-probabilistic proof was...

Rodrigues: Rodrigues formula Leonard James Rogers: Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegő polynomials Schubert polynomial...

Bailey, W. N. (1951), "On the simplification of some identities of the Rogers-Ramanujan type", Proceedings of the London Mathematical Society, Third...

appears in various identities discovered by Srinivasa Ramanujan involving continued fractions. For example, this case of the Rogers–Ramanujan continued fraction:...

number theory, finding deep generalizations and analogs of the Rogers–Ramanujan identities. Ron Cohen Anton Kapustin Ernest Baver Boris Gotkin Umut Gursoy...

others, who proved Ramanujan's statements about them and found several more examples and identities. (Most of the "new" identities and examples were already...

Brenner, Charles H. (November 1986). "Asymptotic Analogs of the Rogers-Ramanujan Identities in Number Theory". Journal of Combinatorial Theory, Series A...

}{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...