Umbral Calculus, Bailey Chains, and Pentagonal Number Theorems
نویسندگان
چکیده
منابع مشابه
AN ELLIPTIC BCn BAILEY LEMMA, MULTIPLE ROGERS–RAMANUJAN IDENTITIES AND EULER’S PENTAGONAL NUMBER THEOREMS
An elliptic BCn generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter BCn Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system BCn are proved as applications, including a 6φ5 summation formula, a generalized Watson transformation and an unspecialized Rogers–Selberg identity. The last ...
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Common ground to the three concepts are special polynomial sequences, called She er sequences. A polynomial sequence (sm (x))m2N0 is a sequence of polynomials sm (x) 2 K [x] such that deg sm = m, s0 6= 0. It is convenient to de ne sm = 0 for negative m. The coe cient ring K is assumed to be an integral domain. For this introduction to Finite Operator Calculus it su ces to choose K as R [!], the...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3111