Biorthogonal polynomials suggested by the Laguerre polynomials

On Bilateral Generating Functions of Konhauser Biorthogonal Polynomials

“…From the above analysis, it is clear that whenever one knows a generating relations of the form (1, 3) then the corresponding bilateral generating relations can at once be written down from (2,4). So one can get a large number of bilateral generating relations by attributing different suitable values to in (1,3).…”

“…In [2], Konhauser also introduced two sets of polynomials { ( ; )} and { ( ; )}, which are biorthogonal with respect to the weight function For = 1, these polynomials reduce to the generalized Laguerre polynomials, ( ). For previous works on these polynomials one can see the works [7][8][9][10][11][12][13][14].…”

q-Konhauser polynomials

“…More recently these polynomials gained a sudden popularity with the interesting work of Konhauser [7,8] and Preiser [10] (see also [2]). In particular the biorthogonal system related to the Laguerre distribution is now known as the Konhauser polynomials.…”

On Generating Functions of Biorthogonal Polynomials Suggested by Laguerre Polynomials

“…An explicit representation for the Konhauser bi-orthogonal polynomials [1], ; , suggested by the Laguerre polynomials was given by carlitz [2] in the following form:…”