We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).

Let K be an effective field of characteristic zero. An effective tribe is a subset of K[[z1, z2, ...]] =K ∪K[[z1]] ∪K[[z1, z2]] ∪ ··· which is effectively stable under the Kalgebra operations, restricted division, composition, the implicit function theorem, as well as restricted monomial transformations with arbitrary rational exponents. Given an effective tribe with an effective zero test, we ...

A new class of distributions motivated by systems having both series and parallel structures is introduced. Some mathematical properties the (including moment generating function, moments order statistics) are derived. Estimation addressed maximum likelihood method performance estimators assessed a simulation study. An illustration using three failure data sets shows usefulness class.

Given a first order autonomous algebraic ordinary differential equation, we present a method to compute all formal series solutions. Furthermore, when the ground field is the field of the complex numbers, the computed formal power series solutions are indeed convergent in suitable neighborhoods. keywordAlgebraic autonomous differential equation, algebraic curve, local parametrization, formal po...

This paper presents a generalized numerical method to evaluate element stiffness matrices needed for the free vibration and stability analyses of non-prismatic columns resting on one- or two-parameter elastic foundations and subjected to variable axial load. For this purpose, power series approximation is used to solve the fourth–order differential equation of non-prismatic columns with v...

in this paper, the homotopy analysis method (ham) is considered to obtain the solution of the schrodinger equation with a power law nonlinearity. for this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region...

The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series.

Data streams are an ideal vehicle for handling power series. Stream implementations can be read off directly from simple recursive equations that define operations such as multiplication, substitution, exponentiation, and reversion of series. The bookkeeping that bedevils these algorithms when they are expressed in traditional languages is completely hidden when they are expressed in stream ter...

The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes of the reduced standard basis of the ideal can be constructed effectively.