Abel's method on summation by parts and terminating well-poised q-series identities
نویسندگان
چکیده
منابع مشابه
ABEL’S METHOD ON SUMMATION BY PARTS AND BALANCED q-SERIES IDENTITIES
The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating balanced basic hypergeometric series. The examples strengthen our conviction that as traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series.
متن کاملOn q-Operators and Summation of Some q-Series
Using Jackson's q-derivative and the q-Stirling numbers, we establish some transformation theorems leading to the values of some convergent q-series.
متن کاملA simple proof of Bailey’s very-well-poised 6ψ6 summation
Using Rogers’ nonterminating 6φ5 summation and elementary series manipulations, we give a simple proof of Bailey’s very-well-poised 6ψ6 summation. This proof extends M. Jackson’s first proof of Ramanujan’s 1ψ1 summation.
متن کاملOrthogonality of Very Well-poised Series
Rodrigues formulas for very well-poised basic hypergeometric series of any order are given. Orthogonality relations are found for rational functions which generalize Rahman’s 10φ9 biorthogonal rational functions. A pair of orthogonal rational functions of type RII is identified. Elliptic analogues of some of these results are also included.
متن کاملSome Remarks on Very - Well - Poised 8 φ 7 Series
Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.10.011