Show that the function represented by the power series is a solution of the differential equation.y=∑limits^( ∞ )_(n=0)(-1)^n(x^(2n))(4^n(n!)^2), x^2y''+xy'+x^2y=0 相关知识点: 试题来源: 解析 We first find the first and second derivatives of yy'=∑limits^( ∞ )_...
百度试题 结果1 题目【题目】Write down the function represented by the power seriesthe interval of convergence is -1x1.∑_(n=1)^∞x^(n-1)wnere 相关知识点: 试题来源: 解析 1/(1-x) 反馈 收藏
We present a sufficient condition of existence of asymptotic expansion in negative power series for a function defined by Taylor series and unitary formulas for coefficients of this expansion. An example of computing scheme for arctangent function is represented.Nikitin, Mihail...
Find the interval of convergence of the power series and find a familiar function that is represented by the power series on that interval. 1 - (x + 3) + (x+ 3)^2 - (x + 3)^3 + . . . . + ...
Let's consider the functiony=ln(1−x). It is known that the Maclaurin series expansion of that function is represented as: ln(1−x)=−x−x22−x33−x44−⋯=−∑n=1∞xnn. To find the radius and interval of convergence of the po...
Convergence of a Power Series Using Geometric Series: A series is represented as a geometric progression known as geometric series. The convergence of the geometric series depends upon the common ratio, that is {eq}\left| r \right| < 1...
Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The...
. Here the difference between residual generation and the estimated state can be represented by a Lyapunov variable V. This is represented as (5.25) Here ρ is defined to minimize the positive definite matrix ℵt. Once the error matrix determines the residual, the evaluation of residual is ...
1 is represented by the Hill function (HF), which is widely used for modelling biological regulations. (See Methods for our detailed implementation). Specifically, we will verify whether the regulation network found by RNN can still achieve the desired function if being converted to an HF-based...
Continental coastlines in ESMs are typically represented by large grid cells; a single cell may encompass an entire estuary. As a result, sediment, carbon, and water delivered to the cells are fully mixed and diluted by the cell size and cannot accommodate complex biogeochemical interactions that ...