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Chapter 12: Q9P (page 584)

Use problem 7 to show that

Plm (x) = (-1)m (l+m)!/(l-m)! (1-x2)/2l! dl-m/dxl-m(x2-1)l

Short Answer

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Step by step solution

01

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

The relation between Plm(x) and Pl(x) is as follow.

Plm(x) =1/2l l! (1-x2)m/2dl+m/dxl+m(x2-1)l ..... (1)

02

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

Write (10.7) with m replaced by -m; then use Problem 7 to show that Pl-m(x) = (-1)m (l-m)!/(l+m)! Plm(x).

Comment: This shows that (10.7) is a solution of (10.1) when m is negative.

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