James Stewart《微积分》笔记·11.9 Representations of Functions as Power Series(函数的幂级数表示) JackLin Lūcem sequor. 本节将研究如何对特定类型的函数通过对几何级数代数变形或进行微分或积分运算以表示成幂级数的形式. 转化为幂级数表示常用于非基本初等函数的反导数,解微分方程以及对函数的多项式近似表示. 一...
ticular, obtain new functions represented as power series. The following answers this question. Result 1.4. If the power series has radius of convergence R ≥ 0, then the function defined by is differentiable and integrable on the interval (a − R, a + R) and where C is some constant...
功能和序列表示 representations of functions andpower series 功能和序列表示
L. Zhongkui, "Triangular matrix representations of rings of generalized power series," Acta Mathematica Sinica (English Series), vol. 22, no. 4, pp. 989-998, 2006.Z.K. Liu, Triangular matrix representations of rings of generalized power series, Acta Math. Sin. (Engl. Ser.) 22 (2006) ...
We develop the SPPS representations for solutions of Sturm–Liouville equations of the formp(x)u′′+q(x)u=∑k=1NλkRku,x∈(a,b)where Rkurk(x)u+sk(x)u′,k=1,…N, the complex-valued functions p, q, rk, sk are continuous on the finite segment a,b. Several numerical examples ...
In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises drivi...
In a previous paper, we developed a power series representation and estimates for an effective action of the formln[∫ef(α1,…,αs;z,z)dμ(z,z)/∫ef(0,…,0;z,z)dμ(z,z)]. Here,f(α1,…,αs;z,z)is an analytic function of the complex fieldsα1(x),…,αs(x),z(x)...
While the Report functions to limit and dismiss any trans affirming perspectives, those from children are not even given space on the page. This actual silencing and dismissal of children’s perspectives within the text of the Report mirrors its constructed subjectivities given that parents, teachers...
formal power series representationslinear fractional transformationsminimalityThe concept of minimality as developed for uncertain and multidimensional systems represented by linear fractional transformations (LFTs) is related to realization theory results for formal power series. We discuss the relationship ...
Vibrations of a liquid with an impedance load at its surface are considered as an auxiliary problem, and, in the framework of this problem, the initial terms of the power series expansions of the integer functions, which appear in the expression for the transient admittance, are determined. ...