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Q. 65

Found in: Page 681


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

The second-order differential equation


where p is a nonnegative integer, arises in many applications in physics and engineering, including one model for the vibration of a beaten drum. The solution of the differential equation is called the Bessel function of order p, denoted by Jp(x). It may be shown that Jp(x) is given by the following power series in x:


Find and graph the first four terms in the sequence of partial sums of Jo(x).

The four terms are 1,1-14x2,1-14x2+164x4,1-14x2+164x4-12304x6

And the graph is

See the step by step solution

Step by Step Solution

Step 1. Given information

An expression is given as Jp(x)=k=0(-1)kk!(k+p)!22k+px2k+p

Step 2. Finding four terms

The Bessel function is given in the order of p. So the value of Jo(x) is


Therefore the first four terms of partial sums are as,


And the graph is

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