Under conditions V3=V5 =0, V7 is reduced to 7 with only 9 terms.刘尊全秦朝斌科学通报(英文版)刘尊全;秦朝斌.MECHANICAL DEDUCTION OF FORMULAS OF DIFFERENTIAL EQUATIONS (I).Science in China,Ser.A.1981Z. Liu,C. Qin.Mechanical deduction of formulas of differential equations(I). Scientia Sinica...
Under consideration are semi-groups generated by certain partial differential operators whose coefficients are polynomials. Product formulas are developed for these semi-groups, involving integral operators and the fundamental solution of the one-dimensional parabolic equation ∂u∂t=((−1)n2−1n!
Abstract We obtain some operator representations for the solutions of differential-difference equations with applications to multidimensional identification problems.This is a preview of subscription content, log in via an institution to check access. ...
We start with a well known result on the solutions of differential Sylvester equations which concerns a more general case of the SLE (where the coefficient matrices may depend on time). Theorem 1 (Existence and Uniqueness of Solutions, [1, Thm. 1.1.1., Thm. 1.1.3., Thm. 1.1.5]) LetI...
Calculus 2 focuses on the mathematical study of change first introduced during the curriculum of Calculus 1. Some of the important topics under Calculus 2 are, Differential Equations Sequence and Series Application of Integrals Trapezoidal RuleandSimpsons Rule ...
These formulas are intended to approximate the calculation of Fourier coefficients of functions under consideration. The explicit formulas for the weights and the errors of optimal cubature formulas are obtained by techniques from functional analysis and partial differential equations.Bulgak Haydar...
Differential Equations Sequence and SeriesImportant Notes on PrecalculusPrecalculus comprises the study of topics that are required to learn about calculus. Algebra and Trigonometry and the two broad categories of topics that fall under precalculus. The topics that fall under precalculus do not focus...
Expansion Formulas for Fractional DerivativesIn this chapter, we present a new numerical tool to solve differential equations involving three types of Caputo derivatives of fractional variable-order. For each one of them, an approximation...doi:10.1007/978-3-319-94006-9_3Ricardo Almeida...
the exterior differential (note that we use a bold letter for the exterior differential to distinguish it from the itô differential d appearing later). denote by x .( x ) a brownian motion on m starting at \(x\in m\) with generator l and explosion time \(\zeta (x)\) . the ...
Differential equations for zp in terms of xp are established in Section 4. The main results occur in Section 5. In Theorem 5.1 each function zp is expressed as a power series in xp, and also in two ways in terms of hypergeometric functions of xp. This gives rise to hypergeometric ...