Results 31 to 40 of about 505,916 (139)
Finite Rogers-Ramanujan Type Identities [PDF]
The Electronic Journal of Combinatorics, 2003 Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a
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Modular relations for the Rogers-Ramanujan-Slater type functions of order fifteen and its applications to partitions [PDF]
Romanian Journal of Mathematics and Computer Science, 2013 In a manuscript of Ramanujan, published with his Lost Notebook [20] there are forty identities involving the Rogers-Ramanujan functions. In this paper, we establish several modular relations involving the Rogers-Ramanujan functions and the Rogers ...
Chandrashekar Adiga +2 more
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Some theorems on the explicit evaluation of Ramanujan's theta-functions
International Journal of Mathematics and Mathematical Sciences, 2004 Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants.
Nayandeep Deka Baruah, P. Bhattacharyya
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A PROBABILISTIC PROOF OF THE ROGERS–RAMANUJAN IDENTITIES [PDF]
Bulletin of the London Mathematical Society, 2001 The asymptotic probability theory of conjugacy classes of the finite general groups leads to a probability measure on the set of all partitions of natural numbers. A simple method of understanding these measures in terms of Markov chains is given in this paper, leading to an elementary probabilistic proof of the Rogers–Ramanujan identities.
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Level two string functions and Rogers Ramanujan type identities
Nuclear Physics B, 2014 The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type G/U(1)r, where G is the algebra at level two and r is its rank.
Arel Genish, Doron Gepner
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The Rogers-Ramanujan Identities [PDF]
, 2015 In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The Rogers-Ramanujan Identities.
Hossain, Fazlee, Das, Sabuj
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On a Combinatorial Result Related to the Rogers-Ramanujan Identities
Trends in Computational and Applied Mathematics, 2000 We give a generating function for partitions with different conditions and a combinatorial proof for a bijection between these partitions and another class of partitions.
J.P.O. Santos, P. Mondek
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A new proof of some identities of Bressoud
International Journal of Mathematics and Mathematical Sciences, 2002 We provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(5m+1)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(5m+3)/2 [ 2N+2N+2m+2], which can be considered as finite versions of the Rogers ...
Robin Chapman
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Arc spaces and the Rogers–Ramanujan identities [PDF]
The Ramanujan Journal, 2012 Let \(f\) be a polynomial in \(n\) variables \(x_1\),\dots, \(x_n\) over a field \(k\) with \(f(0)=0\) and let \(k[[t]]\) be the ring of formal power series in one variable over \(k\). The arc space of the germ of algebraic variety \((X,0)\) defined by \(f\) (i.e.
Bruschek, Clemens +2 more
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A Generalized Inverse Binomial Summation Theorem and Some Hypergeometric Transformation Formulas
International Journal of Combinatorics, Volume 2016, Issue 1, 2016., 2016 A generalized binomial theorem is developed in terms of Bell polynomials and by applying this identity some sums involving inverse binomial coefficient are calculated. A technique is derived for calculating a class of hypergeometric transformation formulas and also some curious q series identities.
S. M. Ripon, Toufik Mansour
wiley +1 more source