An algebraic treatment of the Askey biorthogonal polynomials on the unit circle

A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak {J}$ .

A triple product formula for plane partitions derived from biorthogonal polynomials

International audience A new triple product formulae for plane partitions with bounded size of parts is derived from a combinato- rial interpretation of biorthogonal polynomials in terms of lattice paths. Biorthogonal polynomials which generalize the little q-Laguerre polynomials are introduced to derive a new triple product formula which recovers the classical generating function in a triple product by MacMahon and generalizes the trace-type generating functions in double products by Stanley and Gansner.

Generalization of Konhauser Polynomials

In this paper, we are showing study of biorthogonal polynomials associated with generalization of Laguere polynomials of Srivastava and Singhal [14]. It happens to generalized Konhauser. here we are trying to obtain the generating functions, recurrence relations, biorthogonality relations, integral representations and also bilinear and bilateral generating relations for the new class of biorthogonal system.

Ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients

In this paper we study matrix biorthogonal polynomials sequences that satisfy a nonsymmetric three term recurrence relation with unbounded matrix coefficients. The outer ratio asymptotics for this family of matrix biorthogonal polynomials is derived under quite general assumptions. Some illustrative examples are considered.