On the general Rogers-Ramanujan theorem
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On the general Rogers-Ramanujan theorem

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Published by American Mathematical Society in Providence .
Written in English


  • Number theory.,
  • Partitions (Mathematics),
  • Hypergeometric functions.

Book details:

Edition Notes

Bibliography: p. 86.

Other titlesRogers-Ramanujan theorem.
Statement[by] George E. Andrews.
SeriesMemoirs of the American Mathematical Society, no. 152, Memoirs of the American Mathematical Society ;, no. 152.
LC ClassificationsQA3 .A57 no. 152, QA241 .A57 no. 152
The Physical Object
Pagination86 p.
Number of Pages86
ID Numbers
Open LibraryOL5055547M
ISBN 10082181852X
LC Control Number74018067

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Genre/Form: Electronic books: Additional Physical Format: Print version: Andrews, George E., On the general Rogers-Ramanujan theorem. Providence: American. The objective in this paper is to present a general theorem for overpartitions analogous to Rogers–Ramanujan type theorems for ordinary partitions with restricted successive ranks. View Show Author: Jeremy Lovejoy. Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo 6 Alladi, Krishnaswami and Berkovich, Alexander,, ; Generalizations of the Rogers-Ramanujan identities. Alder, Henry L., Pacific Journal of Mathematics, ; A note on the Rogers-Ramanujan identities Carlitz, L., Duke Mathematical Journal, Cited by:   Abstract: Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain.

functions. In Section 3 some immediate consequences of Theorem are derived, the most interesting one being the new q-series identity claimed in Corollary Section 4 contains a proof of Theorem and Section 5 contains a proof of the A2 Rogers–Ramanujan identities () based on Corollary Finally, in Section 6 we. provide proofs for many of the claims about the Rogers–Ramanujan and generalized Rogers–Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants. 1. Introduction The Rogers–Ramanujan continued fraction, defined by () R(q):= q1.   Furthermore, the Rogers–Ramanujan continued fraction arises from more general continued fractions of quotients of basic hypergeometric series, which we also do not examine in this paper. Unless otherwise stated, page numbers refer to the lost notebook [27]. a priori. However, the classical Caratheodory’s theorem states that one can always take m n+ 1. Theorem (Caratheodory’s theorem). Every point in the convex hull of a set T ˆRn can be expressed as a convex combination of at most n+ 1 points from T. The bound n+1 can not be improved, as it is clearly attained for a simplex T.

  In , Jinhee Yi found many explicit values of the famous Rogers–Ramanujan continued fraction by using modular equations and transformation formulas for theta-functions. In this paper, we use her method to find some general theorems for the explicit evaluations of Ramanujan's cubic continued fraction. On the general Rogers-Ramanujan theorem. Memoir. Amer. Math. Soc. , 86 pp. () pdf16 Applications of basic hypergeometric functions. SIAM Rev. 16(4) () pdf On Rogers-Ramanujan type identities related to the modulus Proc. London Math. Soc. () Theorem 1 (Corrected, p. ). Define, for in closed form a general 2H2 at z= 1, from which one can deduce the following bilateral form of the binomial series theorem. If aand care complex numbers with Re(c of the Rogers–Ramanujan identities (23) and (24). Theorem 2. 3. Ramanujan’s Notebooks The history of the notebooks, in brief, is the following: Ramanujan had noted down the results of his researches, without proofs, (as in A Synopsis of Elementary Results, a book on pure Mathematics, by G.S. Carr), in three notebooks, between the years - .