On Abel-Gontscharoff-Gould's polynomials

نویسندگان

  • Tian-Xiao He
  • Leetsch C. Hsu
  • Peter J. S. Shiue
  • P. J. S. Shiue
چکیده

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples. AMS Subject Classification: 05A10, 11C08, 13F25, 41A58.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On generalization of refinement of Jensen’s inequality using Fink’s identity and Abel-Gontscharoff Green function

In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the 'two-point right focal' problem. We use Fink's identity and a new Abel-Gontscharoff-type Green's function for a 'two-point right focal' to generalize the refinement of Jensen's inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex function to higher o...

متن کامل

Some new families of definite polynomials and the composition conjectures

The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

متن کامل

Fuzzy collocation methods for second- order fuzzy Abel-Volterra integro-differential equations

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

متن کامل

Multivariate Delta Gon£arov and Abel Polynomials

Classical Gon£arov polynomials are polynomials which interpolate derivatives. Delta Gon£arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gon£arov polynomials and univariate delta Gon£arov polynomials to the multivariate setting using umbral calculus. After intro...

متن کامل

Generalized Rook Polynomials

Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials. Connections are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, Abel polynomials and forests, and polynomial sequences of binomial type. Factorization and recipro...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004