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Chapter 8: Q. 5 (page 692)

If the series 鈭�k=0鈭�ckx-x0kconverges to the function hxfor every real number, provide a formula for ck in terms of the function h.

Short Answer

Expert verified

The formula forckishkx0k!.

Step by step solution

01

Step 1. Given Information.

The series 鈭�k=0鈭�ckx-x0kconverges to hxfor every real number.

02

Step 2. Explanation.

The series is converges to the function so, Taylor polynomial for h(x) in the form

鈭�k=0鈭�hkx0k!x-x0k.

For series鈭�k=0鈭�ckx-x0k,role="math" localid="1649601140285" ck=hkx0k!

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Most popular questions from this chapter

What is x0if (p,q)is the interval of convergence for the power series 鈭�k=0鈭�鈥�akx鈭�x0k?

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