共查询到10条相似文献,搜索用时 109 毫秒
1.
Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established. The authors are convinced by the exhibited examples that the iterating machinery based on the modified Abel lemma is powerful and a natural choice for dealing with terminating theta hypergeometric series. 相似文献
2.
The Abel's lemma on summation by parts is employed to evaluate terminating hypergeometric series. Several summation formulae are reviewed and some new identities are established. 相似文献
3.
Four classes of quartic theta hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformations are proved that express the quartic series in terms of well-poised, quadratic and cubic ones. Thirty new summation formulae for terminating quartic theta hypergeometric series are derived consequently. 相似文献
4.
Wenchang Chu 《Mathematical Methods in the Applied Sciences》2019,42(6):1831-1843
A new class of twisted cubic q‐series is investigated by means of the modified Abel lemma on summation by parts. Several remarkable summation and transformation formulae are established for both terminating and nonterminating series. 相似文献
5.
S. O. Warnaar 《Constructive Approximation》2002,18(4):479-502
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating,
balanced, very-well-poised, elliptic hypergeometric series. 相似文献
6.
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms of Jacobi's triple product identity and Watson's quintuple product identity are also proved. 相似文献
7.
We apply multidimensional matrix inversions to multiple basic hypergeometric summation theorems to derive several multiple (q-)series identities which themselves do not belong to the hierarchy of (basic) hypergeometric series. Among these are A terminating and nonterminating q-Abel and q-Rothe summations. Furthermore, we derive some identities of another type which appear to be new already in the one-dimensional case. 相似文献
8.
The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating well-poised basic hypergeometric series, mainly discovered by [F H. Jackson, Certain q-identities, Quart. J. Math. Oxford Ser. 12 (1941) 167–172]. This strengthens further our conviction that as a traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series. 相似文献
9.
An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications 下载免费PDF全文
Yong S. Kim Arjun. K. Rathie Richard B. Paris 《Mathematical Methods in the Applied Sciences》2015,38(18):4891-4900
A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well‐known Saalschütz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijovi? & Miller. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
Wenchang Chu 《Mathematica Slovaca》2012,62(4):689-694
By combining a telescopic summation formula with Kummer-Thomae-Whipple transformation, we prove two nonterminating 3 F 2(1)-series identities with one of them confirming a conjecture by Milgram (2009) and another one extending a couple of terminating series identities due to Gessel and Stanton (1982). 相似文献