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Chapter 12: Q9-1P (page 562)

Expand the following functions in the Legendre series.
$F (x) = [\begin{matrix} - 1 & - 1 & \leq & x & 0 \\ 1 & 0 & \leq & x & 1 \end{matrix}]$

Short Answer

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Step by step solution

01

Concept of Legendre polynomial

02

Simplify the expression

03

Substitute for the value of m and P0(x)

04

Substitute for the value of m and P1(x)

05

Substitute for the value of m and P2(x)

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Most popular questions from this chapter

To sketch the graph of $\sqrt{x} J_{\frac{1}{2}} (x)$ for x from 0 to $π$ .

To study the approximations in the table, a computer plot on the same axes the given function together with its small x approximation and its asymptotic approximation. Use an interval large enough to show the asymptotic approximation agrees with the function for large x . If the small x approximation is not clear, plot it alone with the function over a small interval $N2(x)$ .

To show the following equation shown in the problem

$2 \frac{d}{d x} J_{a} (x) = J_{a - 1} (x)$ .

From (17.4), show that, $h_{n}^{(1)} (ix) = - e^{- x} / x$ .

See all solutions

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