This paper focuses on the establishment of a new subfamily analytic functions including Touchard polynomials. Then, we attempt to obtain geometric properties such as coefficient inequalities, distortion properties, extreme points, radii starlikeness and convexity, partial sums, neighbourhood results integral means’ inequality for this class. The symmetry established in current may be examined f...

Abstract The Hilbert class polynomial has as roots the j -invariants of elliptic curves whose endomorphism ring is a given imaginary quadratic order. It can be used to compute over finite fields with prescribed number points. Since its coefficients are typically rather large, there been continued interest in finding alternative modular functions corresponding polynomials smaller. Best known Web...

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

It has been known since 2007 that the Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L1 of H in terms of an eigenbas...

We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U ⊗ w or w ⊗ U , where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2 1). We show that the set S contains exactly one symmetry class S0 ∈ S whose ...

Hikita polynomials are the combinatorial side of the rational shuffle theorem. Building upon a recent formula for (m, 3)-Catalan polynomials, we prove a formula for (m, 3)-Hikita polynomials in terms of Catalan polynomials. This formula shows a surprising relation among coefficients of Hikita polynomials and implies deeper recursive relations and proves the q, t-symmetry of (m, 3)-Hikita polyno...

An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while μ(G) is the cardinality of a maximum matching. If sk is the number of independent sets of cardinality k in G, then I(G;x) = s0 + s1x+ s2x 2 + ...+ sαx , α = α (G) , is called the independence polynomial of G ...