Results 11 to 20 of about 505,916 (139)

IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE [PDF]

International Journal of Number Theory, 2007
It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2)54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new
Sills, Andrew V.
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New finite Rogers-Ramanujan identities [PDF]

The Ramanujan Journal, 2009
We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.
Guo, Victor J. W., Jouhet, Frederic, Zeng, Jiang   +2 more
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Bilateral identities of the Rogers–Ramanujan type [PDF]

Transactions of the American Mathematical Society, Series B, 2023
We derive by analytic means a number of bilateral identities of the Rogers–Ramanujan type. Our results include bilateral extensions of the Rogers–Ramanujan and the Göllnitz–Gordon identities, and of related identities by Ramanujan, Jackson, and Slater.
Schlosser, Michael J.
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Rogers-Ramanujan-Slater Type Identities [PDF]

The Electronic Journal of Combinatorics, 2008
In this survey article, we present an expanded version of Lucy Slater's famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the publication of Slater's papers, and older identities (such as those in Ramanujan's lost notebook) which were not included in Slater's papers.
McLaughlin, James, Sills, Andrew V., Zimmer, Peter   +2 more
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The Rogers-Ramanujan Identities and Cauchy's Identity

Symmetry, Integrability and Geometry: Methods and Applications
The Rogers-Ramanujan identities are investigated using the Cauchy identity for Schur functions.
Stanton, Dennis
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On identities of the Rogers-Ramanujan type [PDF]

Journal of Mathematical Analysis and Applications, 1985
The author proves two transformation formulae for q-series: \[ \sum a_ k\left[ \begin{matrix} a+b\\ a+k\end{matrix} \right] \left[ \begin{matrix} a+b\\ b+k\end{matrix} \right]=\sum \frac{(q)_{a+b} q^{j^ 2} S_{2j}}{(q)_{a-j} (q)_{b-j} (q)_{2j}} \] where \(S_{2j}=\sum \left[ \begin{matrix} 2j\\ j+k\end{matrix} \right] q^{-k^ 2} a_ k\), and \[ \sum b_ k ...
Paule, Peter
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Bilateral Bailey lemma and Rogers–Ramanujan identities [PDF]

Advances in Applied Mathematics, 2009
The authors prove a bilateral Bailey lemma and apply it together with classical summation theorems for bilateral basic hypergeometric series to derive twenty-five transformation formulas (T1)--(T25) between unilateral and bilateral series. The transformations are used to establish and tabulate 200~identities of Rogers--Ramanujan type, that is, series ...
CHU, Wenchang, ZHANG W.
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Refinements of the Rogers–Ramanujan Identities [PDF]

Experimental Mathematics, 2015
Refinements of the classical Rogers-Ramanujan identities are given in which some parts are weighted. Combinatorial interpretations refining MacMahon's results are corollaries.
Kathleen M. O'Hara, Dennis Stanton
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On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity [PDF]

Mathematica Moravica, 2020
The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18].
Chaudhary M.P., Chaudhary Sangeeta
doaj   +1 more source

Variations on a result of Bressoud [PDF]

, 2013
The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years ...
Kurşungöz, Kağan, Sellers, James A.
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