Related papers: Elementary derivations of identities for bilateral…
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…
In this paper, we establish two new transformation formulas for ${}_{8}\psi_{8}$ and ${}_8\phi_7$ series by means of Slater's general transformation for bilateral series. As applications, some specific transformation formulas are presented…
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our…
The classical summation and transformation theorems for very well-poised hypergeometric functions, namely, $_{5}F_4(1)$ summation, Dougall's $_{7}F_6(1)$ summation, Whipple's $_{7}F_6(1)$ to $_{4}F_3(1)$ transformation and Bailey's…
We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials,…
We derive two generalizations of Gasper's transformation formula for basic hypergeometric series. Using these generalized formulas, we give explicit expressions for the coefficients of three-term relations for the basic hypergeometric…
In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of…
We prove a master theorem for hypergeometric functions of Karlsson-Minton type, stating that a very general multilateral U(n) Karlsson-Minton type hypergeometric series may be reduced to a finite sum. This identity contains the…
Lucy Slater used Bailey's $_6\psi_6$ summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type. In the present paper we apply the same techniques to Chu's…
A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…
Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised 8phi7 series. In this paper we use this fact to derive various basic hypergeometric and…
By applying Slater's transformation formulas for the bilateral basic hypergeometric series ${}_2\psi_{2}$, we derive three type translation formulas for the generalized Zwegers' $\mu$-function (``continuous $q$-Hermite function'') which was…
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.
We establish a number of extensions of the well-poised Bailey lemma and elliptic well-poised Bailey lemma. As application we prove some new transformation formulae for basic and elliptic hypergeometric series, and embed some recent…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's $_6\psi_6$-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations…
In terms of Dougall's $_2H_2$ series identity and the series rearrangement method, we establish an interesting symmetric formula for hypergeometric series. Then it is utilized to derive a known nonterminating form of Saalsch\"{u}tz's…
In this paper we introduce the so-called truncated very-well-poised $_6\psi_6$ series and set up an explicit recurrence relation for it by means of the classical Abel lemma on summation by parts. This new recurrence relation implies an…
Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…
We list $A_n$, $C_n$ and $D_n$ extensions of the elliptic WP Bailey transform and lemma, given for $n=1$ by Andrews and Spiridonov. Our work requires multiple series extensions of Frenkel and Turaev's terminating, balanced and…