By the help of generating functions and their functional equations, we derive some new formulas and relations involving the Bernoulli polynomials, the Euler polynomials, and the Genocchi polynomials.doi:10.1063/5.0162337Yagmur CetinYilmaz SimsekAIP Publishing LLCAIP Conference Proceedings
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PolynomialsA polynomial is an algebraic expression that consists of variables, coefficients, andconstants that are joined using algebraic operations like addition, multiplication, positive exponentiation, etc.The list of polynomial topics that fall under precalculus are given below:...
In [3] a formula for the class of the structure sheaf of a general quiver variety is proved, which expresses this class as a linear combination of products of stable Grothendieck polynomials for Grassmannian permutations. Furthermore, it is conjectured that the quiver coefficients occurring in...
In order to give our results, we need the following properties and definitions for generating functions of the special numbers and polynomials. In addition,p-adic integrals and their properties, which have many valuable applications in almost all areas of mathematics as well as mathematical physics,...
We find approximate expressions and for the real and imaginary parts of the th zero of the Bessel polynomial . To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros
A.A. Adamov, On the asymptotic expansion of the polynomials \(e^{ax^{2}/2 }d^{n}[e^{(-ax^{2}/2) }]/dx^{n}\) for large values of n ( in Russian ). Ann. Polytech. Inst. St. Petersb. 5, 127–143 (1906) Google Scholar H. Aikawa, Infinite order sobolev spaces, analy...
5. Polynomials: A expression containing two or more terms is known as a polynomial. It includes Binomials, Trinomials, Quadrinomials, and all the Algebraic expressions with five or more terms.Algebraic Expressions Based on Highest Degree of Terms...
Let j(τ), xp and Δp be as defined in Section 2, and let fp and gp be the polynomials defined in Table 1. Thenj(τ)=12xpp(fp(xp)−gp(xp)Δp1/2(xp)) andj(pτ)=12xpp(fp(xp)+gp(xp)Δp1/2(xp)). Moreover,f32(x)−g32(x)Δ3(x)=4x2(1+192x)3,f72(x)−...
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