Suppose that dim R = 0.If f(X) S[[X]]is integral over R[[X]], then every coefficient of f(X) is integral over R. (2) Let dim R 1. There exists a ring S containing R and a power series f(X) S[[X]]such that f(X) is integral over R[[X]], but not all ...
5. Give a power series representation for the integral of the following function.h(x)=(x^4)/(9+x^2) Hint: Integrating this function seems like (potentially) a lot of work, not to mention determining a power series representation of the result. It's a good think that we know how to...
53 This infinite series is the best thing you'll see today【这个无穷级数是你今天会看到的最好的东西】 06:39 What are the residues of the gamma function【伽玛函数的余数是什么】 07:28 A RIDICULOUSLY AWESOME DOUBLE INTEGRAL【一个可笑的可怕的二重积分】 10:57 Thank you for this wonderful ...
20:22 A very interesting differential equation【一个非常有趣的微分方程】 10:03 A nice integral result【一个很好的积分结果】 11:59 积分学中最难的问题之一:Coxeter积分 25:33 Sum of a beautiful infinite series using 2 methods【用两种方法对美丽的无穷级数求和】 14:17 MONSTER INTEGRAL【怪物型积分...
这里引入一个方法,叫做幂级数法(The method of power series)去算这个积分,要做到这个,首先我要用麦克劳林级数(Maclaurin Series)对arctanx做一次幂级数展开。但是如果想要直接套用公式去展开arctan是很困难的,所以我要使用一点点的小trick。 ddx(arctanx)=11+x2=1−x2+x4−x6+... 所以, arctan...
Evaluate the indefinite integral as a power series. Evaluate the given integral by expressing the integrand as Power Series: integral of cos x^4 dx. Evaluate the indefinite integral as a power series. \int \tan^{-1} y^6 dy Evaluate the indefinite integral as a power se...
Evaluate the indefinite integral as a power series. ∫t1−t9dt C+∑n=0∞ What is the radius of convergence R? R = The radius of Convergence of any Binomial Series: Ifkis any number and|x|<1then Binomial series expansion is given as: ...
摘要原文 1. Let be an integral function, λ n being a strictly increasing sequence of nonnegative integers. We shall use the notations describing M ( r ) as the maximum modulus, m ( r ) as the minimum modulus and μ( r ) as the maximum term of f ( z ). ...
Definite Integral; Power Series Representation:Most of the time, the value of a definite integral can be easily obtained by deriving the antiderivative for the integrand function then using the fundamental theorem of calculus. But sometimes it becomes very...
a) Use a power series to approximate the definite integral. int_0^{2.1}xarctan(2x) dx b) Find a power series representation for the function. f(x)=frac{x}{2x^2+1} Use a power series to approximate the definite integral to six decimal places. Integral from 0 to ...