Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials extensions have been introduced investigated. In this paper, we modify the known generating functions polynomials, due to both Milne-Thomsons Dere-Simsek, introduce new class present some involved properties. As obvious special cases newly also power sum-Laguerre-Hermite ...

00 (— l)k (1.2) m-Y,}L-rLt**, k=0 r k where t takes on the values 00 t = £ cm_¡xm-' (cj in GF(p»)). j'-o Then \p(t) has the linearity properties (1.3) W + u) m + *(u), Hct) = ok(t), for arbitrary c in GF(pH); further from (1.2) it follows that (1.4) ik(xt) = ^"(t) x^(t). In turn (1.4) implies the general relation (1.5) (l)^(Mt) =«*(*(*)), where M is a polynomial in GF(pn) of degree m in x, and

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interest...

This paper explores the geometric structure of spectrahedral cone, called symmetry adapted positive semidefinite (PSD) and Gram spectrahedron a symmetric polynomial. In particular, we determine dimension PSD describe its extremal rays, discuss matrix representations. We also consider spectrahedra for specific families polynomials including binary polynomials, quadratics, ternary quartics sextic...

*Correspondence: [email protected] 3Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Republic of Korea Full list of author information is available at the end of the article Abstract We use the p-adic q-integral and group action to count the number of the generating functions of modified q-Euler polynomials in a prescribed set. Some generating function yield...

Let p be a fixed prime number. Throughout this paper Zp, Qp, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp. For x ∈ Cp, we use the notation x q 1 − q / 1 − q . Let UD Zp be the space of uniformly differentiable functions on Zp, and let vp be the normalized exponential valuation of Cp wi...