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Chapter 12: Q 9-2P (page 562)

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

Short Answer

Expert verified

Step by step solution

Concept of Legendre polynomial

Simplify the expression

Substitute for the value of m and P0(x)

Substitute for the value of m and P1(x)

Substitute for the value of m and P2(x)

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Most popular questions from this chapter

Determine the solution of the differential equations.

(a) $x y^{'}' = y$

(b) $y^{'}' - x^{4} y = 0$

Find the norm of each of the following functions on the given interval and state the normalized function $P_{2} (x) on (- 1, 1)$

Use the Section 15 recursion relations and (17.4) to obtain the following recursion relations for spherical Bessel functions. We have written them for $j_{n}$ , but they are valid for $y_{n}$ and for the $h_{n,} (\frac{d}{dx}) j_{n} (x) = {nj}_{n} (x) / x - j_{n + 1} (x)$ ,.

Expand each of the following polynomials in a Legendre series. You should get the same results that you got by a different method in the corresponding problems in Section 5.

7x⁴-3x+1

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 $j2(x)$

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Expand the following functions in Legendre series.F(x)=[0-1≤x0x0≤x1]

Short Answer

Step by step solution

Concept of Legendre polynomial

Simplify the expression

Substitute for the value of m and P0(x)

Substitute for the value of m and P1(x)

Substitute for the value of m and P2(x)

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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