11 papers · 1 filter
Bilinear generating functions of the multivariable Al-Salam-Carlitz polynomials and applications
Qi Chen, Xinrong Ma, Jin Wang
In this paper, by the method of comparing coefficients, we establish a new generating function of multivariable Al-Salam-Carlitz polynomials which contains both Rogers' and Bowman'…
Some q-Identities derived by the ordinary derivative operator
Jin Wang, Ruiqi Ruan, Xinrong Ma
In this paper, we investigate applications of the ordinary derivative operator, instead of the -derivative operator, to the theory of -series. As main results, many new summa…
Dual forms of the orthogonality relations of some classical q-orthogonal polynomials
Qi Chen, Xinrong Ma, Jin Wang
In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete a…
A new recurrence relation for the truncated very-well-poised series and Bailey's summation formula
Jin Wang, Xinrong Ma
In this paper we introduce the so-called truncated very-well-poised series and set up an explicit recurrence relation for it by means of the classical Abel lemma on summati…
Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula
Jin Wang, Xinrong Ma
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the p…
Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities
Jin Wang, Xinrong Ma
In this paper, we introduce the so-called elliptic Askey-Wilson polynomials which are homogeneous polynomials in two special theta functions. With regard to the significance of pol…
A general q-expansion formula based on matrix inversions and its applications
Jin Wang
In this paper, by use of matrix inversions, we establish a general -expansion formula of arbitrary formal power series with respect to the base $$\left\{z^n\frac{(az:q)_n…
Further results on Andrews--Yee's two identities for mock theta functions and
Jin Wang, Xinrong Ma
In this paper, by the method of comparing coefficients and the inverse technique, we establish the corresponding variate forms of two identities of Andrews and Yee for mock theta f…
On Andrews--Warnaar's identities of partial theta functions
Jin Wang, Xinrong Ma
In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar,…
Proof of the --inversion formula conjectured by Hsu and Ma
Jin Wang, Xinrong Ma
In light of the well-known fact that the th divided difference of any polynomial of degree must be zero while ,the present paper proves the -inversion formula co…
Expansion Formulas of Basic Hypergeometric Series via the (1-xy,y-x)--Inversion and Its Applications
Jin Wang, Xinrong Ma
With the use of the -matrix inversion under specializations that , we establish an -expansion formula. When specialized to basic hypergeometric ser…