In this paper, summation formulae for the 2-variable Legendre polynomials in terms of certain multi-variable special polynomials are derived. Several summation formulae for the classical Legendre polynomials are also obtained as applications. Further, Hermite-Legendre polynomials are introduced and summation formulae for these polynomials are also established.

The aim of this paper is to construct generating functions for new families special polynomials including the Appel polynomials, Hermite-Kamp\`e de F\`eriet Milne-Thomson type parametric kinds Apostol numbers and polynomials. Using Euler's formula, relations among functions, Hermite-type Chebyshev Dickson are given. their functional equations, various formulas identities With help computational...

In this paper, we present generalization of matching extensions in graphs and we derive combinatorial interpretation of wide classes of orthogonal and q-orthogonal polynomials. Specifically, we assign general weights to complete graphs, cycles and chains or paths defining matching extensions in these graphs. The generalized matching polynomials of these graphs have recurrences defining various ...

It is often the case that the exact moments of a statistic of the continuous type can be explicitly determined, while its density function either does not lend itself to numerical evaluation or proves to be mathematically intractable. The density approximants discussed in this article are based on the first n exact moments of the corresponding distributions. A unified semiparametric approach to...

We compare results of Birch and Merriman (1972), Győry (1973, 1974) Evertse (1991, 2017), which imply in a precise form that polynomials $\mathbb {Z} [X]$ given discriminant lie finitely many ${\rm GL}_2(\mathbb )$-equivalen

This paper presents a new algorithm for personal identification from their Electrocardiograms (ECG) which is based on morphological descriptors and Hermite Polynomials Expansion coefficients (HPEc). After preprocessing, we extracted ten morphological descriptors which were divided into homogeneous groups (amplitude, surface interval and slope) and we extracted sixty Hermite Polynomials Expansio...

Recently, Tremblay, Gaboury and Fugère introduced a class of the generalized Bernoulli polynomials (see Tremblay in Appl. Math. Let. 24:1888-1893, 2011). In this paper, we introduce and investigate an extension of the generalized Apostol-Euler polynomials. We state some properties for these polynomials and obtain some relationships between the polynomials and Apostol-Bernoulli polynomials, Stir...