Let K be a number field, S a finite set of places of K, and OS be the ring of S-integers. Moreover, let Gn(0)Zd++Gn(d1)Z+Gn(d)be a polynomial in Z having simple linear recurrences of integers evaluated at n as coefficients. Assuming some technical conditions we give a ...
Radicals of polynomial functions, like √(4 – x2), Rational powers of the form n/2, e.g. (x2 + 1)(3/2). Although trig substitution is fairly straightforward, you should use it when more common integration methods (like u substitution) have failed. The technique is very similar to ...
A simple and systematic method is described for calculating the integral of a polynomial function over an arbitrary nonconvex polyhedron. First a general formula is presented for direct evaluation of the integral of a polynomial over a 3-D simplex. An integral over a polyhedron can then be easil...
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We show that testing r-variate polynomials with integer coefficients for irreducibility is m-reducible in polynomial time of the total degree and the largest coefficient length to testing bivariate polynomials for irreducibility. Factoring r-variate polynomials into irreducibles is polynomial time Turing-...
SOMEINTEGRALINEQUALITIESFORTHEPOLARDERIVATIVEOFAPOLYNOMIAL Ana1.TheoryApp1.Vo1.27,No.4(2011),340-350DOI10.1007/s10049.011-034O-8SoMEINTEGRALINEQUALITIESFORTHEPoLARDERLTIVEOFAPOLYNoMIALAbdullahMir(Kashmir.University,India)SajadAminBaba(Govt.Hr.Sec.Institute,India)ReceivedOct.9,2010@EditorialBoardofAnalysisin...
Polynomial Sequences of Binomial Type and Path Integrals Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the\numbral calculus of enumerative combinatorics. We express $p_n(x)$ as a\n\\emph{path integral} in the ``phase space'' $\\Space{N}{} imes {[-\\pi...
We present an algorithm to factorize polynomials in several variables with integral coefficients that is polynomial-time in the degrees of the polynomial t... K A.,Lenstra - 《Theoretical Computer Science》 被引量: 86发表: 1984年 A Generalization of Kharitonov's Four Polynomial Concept for Robus...
Some relations between Bernoulli polynomial and Eurler polynomial; 几个Bernoulli多项式和Euler多项式的关系式 3. In this paper,the Akiyama-Tanigawa algorithm for Bernoulli polynomials and Euler polynomials was investigated,a new kind of closed formulae for Bernoulli polynomials and Euler polynomials are ...
If p/q is a rational zero of a polynomial P(x) with integral coefficients,then p is a factor of a0 (the constant term) and q is a factor of aN (the leading coefficient).除此以外,我只知道这是一个叫做Rational zero(root) theorem 的定理。