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Chapter 12: Q 7-5P (page 562)

Short Answer

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Step by step solution

01

Concept of Legendre polynomial

02

Simplify the equation by Legendre polynomial

03

Consider the left-hand side and evaluate it

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Most popular questions from this chapter

From equation (15.4) show that ∫0∞J1(x)dx=∫0∞J3(x)dx=...=∫0∞J2n+1(x)dx and

∫0∞J0(x)dx=∫0∞J2(x)dx=...=∫0∞J2x(x)dx. Then, by Problem 7, show that

∫0∞Jn(x)dx=1for all integral.n.(15.4)Jp-1(x)-JP+1(x)=2Jp'(x) .

Expand the following functions in Legendre series.

Usingverify (22.19)and (22.20)also findL3(x)andL4(x).

Expand the following functions in Legendre series.

F(x)=[0-1≤x0x0≤x1]

For Problems 1 to 4, find one (simple) solution of each differential equation by series, and then find the second solution by the "reduction of order" method, Chapter 8, Section .

(x-1)y''-xy'+y=0
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