IDENTITIES OF THE ROGERS–RAMANUJAN–SLATER TYPE
نویسندگان
چکیده
منابع مشابه
the investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
The Abel-Type Polynomial Identities
The Abel identity is (x + y) = n ∑ i=0 ( n i ) x(x − iz)i−1(y + iz)n−i, where x, y and z are real numbers. In this paper we deduce several polynomials expansions, referred to as Abel-type identities, by using Foata’s method, and also show some of their applications.
متن کاملFinite Rogers-Ramanujan Type Identities
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 Maple package which is available for free do...
متن کاملShort and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type
New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping. AMS Subject Classification. 05A19; secondary 11B65, 05A17
متن کاملCombinatorics of Ramanujan-Slater Type Identities
We provide the missing member of a family of four q-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in “Identities of the Ramanujan-Slater type related to the moduli 18 and 24,” [J. Math. Anal. Appl. 344/2 (2008) 765–777].
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2007
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042107000912