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Chapter 12: Q9P (page 584)

Use problem 7 to show that
P_l^m (x) = (-1)^m (l+m)!/(l-m)! (1-x²)/2^l! d^l-m/dx^l-m(x²-1)^l

Short Answer

Expert verified

The answer is stated below.

Step by step solution

Relation between Plm(x) and Pl(x):

The relation between P_l^m(x) and P_l(x) is as follow.

P_l^m(x) =1/2^l l! (1-x²)^m/2d^l+m/dx^l+m(x²-1)^l ..... (1)

Put the values in the equation (1):

Putting the above given equation in equation (1) and obtain the solution as follows:

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Most popular questions from this chapter

To study the approximations in the table, 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 $J2(x)$ .

To show that $\lim_{x \to 0} x^{- 3 / 2} J_{3 / 2} (x) = 3^{- 1} \sqrt{2 / π}$ .

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

To study the approximations in the table, 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 agreeing with the function for large x . If the small x approximation is not clear, plot it alone with the function over a small interval $J3(x)$

Verify equation (18.3) i.e. $l \frac{d^{2} θ}{{dl}^{2}} + 2 \frac{dθ}{dl} + \frac{g}{V^{2}} θ = 0$

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Use problem 7 to show thatPlm (x) = (-1)m (l+m)!/(l-m)! (1-x2)/2l! dl-m/dxl-m(x2-1)l

Short Answer

Step by step solution

Relation between Plm(x) and Pl(x):

Put the values in the equation (1):

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Use problem 7 to show that
P_l^m (x) = (-1)^m (l+m)!/(l-m)! (1-x²)/2^l! d^l-m/dx^l-m(x²-1)^l