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Chapter 8: Q-14E (page 434)

Question:In Problem find the first three nonzero terms in the power series expansion for the product f(x)g(x).

Short Answer

Expert verified

The required product is, f(x).g(x)=1.

Step by step solution

01

Given power series expansion

The series expansion of the given series is given by

02

Find the product of the power series expansion

Multiplying both the series

There is only one non-zero term in the series expansion, that is f(x).g(x)=1.

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Most popular questions from this chapter

Use Table 6.4.1 to find the first three positive eigen values and corresponding eigen functions of the boundary-value problem\(xy'' + y' + \lambda xy = 0,y(x),y'(x)\)bounded as \(x \to {0^ + },y(2) = 0\). (Hint: By identifying \(\lambda = {\alpha ^2}\), the DE is the parametric Bessel equation of order zero.)

Question:7. Sometimes the ratio test (Theorem 2) can be applied to a power series containing an infinite number of zero coefficients, provided the zero pattern is regular. Use Theorem 2 to show, for example, that the series

has a radius of convergence , if

and that

has a radius ofconvergence, if

In problems 1-6, determine the convergence set of the given power series.

∑n=0∞3nn!xn

Question: In Problems 1–10, determine all the singular points of the given differential equation.

7. (sinx)y"+(cosx)y =0

Question: In Problems 29–34, determine the Taylor series about the point X0for the given functions and values of X0.

32. f(x)=ln(1+x), x0 =0

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