Finding mixed families of special polynomials associated with Appell sequences

Determinant approach to the 2-Iterated q-Appell and mixed type q-Appell polynomials

In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant definitions for the 2-iterated q-Appell family and for the 2-iterated and mixed type q-Appell polynomials are established. The graphs of some 2-iterated q-Appell and mixed type q-Appell polynomials are drawn for different values of indices and the roots of these polynomials are also investigated for certain values of index n by using Matlab. Finally, the ap…

Explicit formulas for parametrized families of irreducible algebraic Appell, Lauricella and Horn functions

For suitable choices of the parameters the Appell, Lauricella and Horn functions are algebraic. In a previous paper we showed that there exist families of algebraic functions for the F_4, F_C, G_3, H_4, H_5 and H_7 functions, depending on one parameter r. For each of these we give a solution of the form f^r.g of the system of differential equations and give formulas for f and g.

Wronskian Appell Polynomials and Symmetric Functions

We study Wronskians of Appell polynomials indexed by integer partitions. These families of polynomials appear in rational solutions of certain Painlevé equations and in the study of exceptional orthogonal polynomials. We determine their derivatives, their average and variance with respect to Plancherel measure, and introduce several recurrence relations. In addition, we prove an integrality conjecture for Wronskian Hermite polynomials previously made by the first and last authors. Our proofs all exploit strong connections with the theory of symmetric functions.

一种用于单项式性与运算方法的线性代数方法

A Linear Algebra approach to monomiality and operational methods

该研究利用线性代数方法推导多项式空间线性算子的一般结论，证明单项式性关联算子均为带多项式系数的微分算子，并分析了多类经典多项式序列对应的单项式算子。

Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer

We study mixed weighted weak-type inequalities for families of functions, which can be applied to study classical operators in harmonic analysis. Our main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C. Perez, Weighted weak-type inequalities and a conjecture of Sawyer, Int. Math. Res. Not., V. 30, 2005, 1849-1871.