Summation Formulas for Basic Hypergeometric Series

Gasper, George

doi:10.1137/0512020

Cited by 30 publications

(28 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gasper [15,Eq. (19)], found q-analogues of Karlsson and Minton's summations and also extended them to transformation formulae.…”

Section: 3)])mentioning

confidence: 99%

Elementary derivations of identities for bilateral basic hypergeometric series

Schlosser

2003

Sel. math., New ser.

View full text Add to dashboard Cite

We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For motivation, we review our previous simple proof (Proc. Amer. Math. Soc. 130 (2002), 1103-1111) of Bailey's very-wellpoised 6 ψ 6 summation. Using a similar but different method, we now give elementary derivations of some transformations for bilateral basic hypergeometric series. In particular, these include M. Jackson's very-well-poised 8 ψ 8 transformation, a very-well-poised 10 ψ 10 transformation, by induction, Slater's general transformation for very-well-poised 2r ψ 2r series, and Slater's transformation for general r ψr series. Finally, we derive some new transformations for bilateral basic hypergeometric series of a specific type. Mathematics Subject Classification (2000). Primary 33D15.

show abstract

“…Gasper [15,Eq. (19)], found q-analogues of Karlsson and Minton's summations and also extended them to transformation formulae.…”

Section: 3)])mentioning

confidence: 99%

Elementary derivations of identities for bilateral basic hypergeometric series

Schlosser

2003

Sel. math., New ser.

View full text Add to dashboard Cite

show abstract

“…2 (we use Theorem 5 for k = 2 and j = 0). However, as stated in Theorem 1 in the introduction, we proved A (2) s,2n = R s,2n = (n!) 2 n s 2 in [5].…”

Section: It Follows Thatmentioning

confidence: 54%

“…For example, we will show how (1) can be derived from Saalcshütz's identity. Jim Haglund [4] suggested that (1) should follow from Gasper's transformation [2] of hypergeometric series of Karlsson-Minton type. This is indeed the case but we will not include such a derivation in this paper since (1) is a special case of wider class of identities that arise by studying the problem of enumerating permutations according to the number of pattern matches where the equivalence classes of the elements modulo k for k ≥ 2 are taken into account, see [6].…”

Section: Introductionmentioning

confidence: 99%

Classifying Descents According to Equivalence mod k

Kitaev¹,

Remmel²

2006

Electron. J. Combin.

View full text Add to dashboard Cite

In [5] the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the first or the second element in a descent pair is equivalent to k mod k ≥ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results and state a number of open problems.

show abstract

“…For n-pairs of complex parameters {x κ , y κ } satisfying the conditions of Theorem 4, there holds the following bilateral series identity: This bilateral series identity contains several known summation formulae appeared in [5,9,12,14] as special cases, which concern classical and basic hypergeometric series of KarlssonMinton-type with integral parameter differences.…”

Section: Corollary 6 (Chu [6 Theorem 2])mentioning

confidence: 96%

Basic bilateral very well-poised series and Shukla's ψ88-summation formula

Chu

Wang

2007

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

By means of Jackson's q-Dougall-Dixon formula on terminating very well-poised hypergeometric series, the linearization lemma on the factorial fractions with well-poised parameter-pairs will be established. It will be applied to prove the generalized well-poised 8 ψ 8 -series and 10 ψ 10 -series identities. The linearization method will further be employed to present a constructive proof of Milne's transformation formula from nonterminating very well-poised bilateral series to terminating multiple unilateral series.

show abstract

Summation Formulas for Basic Hypergeometric Series

Cited by 30 publications

References 6 publications

Elementary derivations of identities for bilateral basic hypergeometric series

Elementary derivations of identities for bilateral basic hypergeometric series

Classifying Descents According to Equivalence mod k

Basic bilateral very well-poised series and Shukla's ψ88-summation formula

Contact Info

Product

Resources

About