Constant term identities of Forrester-Zeilberger-Cooper

Kaneko, Jyoichi

doi:10.1016/s0012-365x(96)00098-2

Cited by 10 publications

(12 citation statements)

References 8 publications

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“…Our final application of the theory of Macdonald polynomials will be to transformation and summation formulae for bilateral 2 Ψ 2 series. We begin with the following important result of Kadell and Kaneko [14,11,16] which is equivalent to the 1 Ψ 1 summation theorem given above Theorem 6.2 Given a partition λ ∈ P let…”

Section: ψ 2 Transformationsmentioning

confidence: 99%

Transformation formulas for multivariable basic hypergeometric series

Baker¹,

Forrester²

1999

Methods and Applications of Analysis

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We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's 2 φ 1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula and Sear's transformation for terminating, balanced 4 φ 3 series. For bilateral series, we rederive Kaneko's analogue of the 1 ψ 1 summation formula and give multivariable extensions of Bailey's 2 ψ 2 transformations.Dedicated to Dick Askey on the occasion of his 65'th birthday.

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Section: ψ 2 Transformationsmentioning

confidence: 99%

Transformation formulas for multivariable basic hypergeometric series

Baker¹,

Forrester²

1999

Methods and Applications of Analysis

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“…This integration formula in turn gives explicit formulae of the values of 2^i 9 ' (a, b; c; x) at special points (Proposition 5.4). In a separate paper [Kan3] we shall show that Theorem 4.11 implies the constant term identities due to Forrester, Zeilberger and Cooper [F, Z, C].…”

Section: R(rr+^+(2n-^-l)fc)r(l+fc) -mentioning

confidence: 99%

$q$-Selberg integrals and Macdonald polynomials

Kaneko¹

1996

Ann. Sci. École Norm. Sup.

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“…Rosengren ( ) Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden e-mail: hjalmar@math.chalmers.se In Theorem 3.1 we give an elliptic extension of a multivariable Bailey transformation recently discovered by Kajihara [12]. In contrast to most known transformations, Kajihara's identity relates sums of different dimension; see [8,14,15,20,21] for further results with this property. (The reference [14] was kindly pointed out by the referee.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to most known transformations, Kajihara's identity relates sums of different dimension; see [8,14,15,20,21] for further results with this property. (The reference [14] was kindly pointed out by the referee. ) We mention that, in view of the analogy between hypergeometric series and hypergeometric integrals, there may exist related transformations between integrals of different dimension.…”

Section: Introductionmentioning

confidence: 99%