Chapter 12: Q 8-4P (page 562)
Find the norm of each of the following functions on the given interval and state the normalized function
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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
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 7 (e).
Substitute the P1(x)you found in Problems 4.3 or 5.3 into equation (10.6)to find, Plm(x); then let x=cos θto evaluate:
P32(cosθ)
We obtained (19.10) forIt is, however, valid for, that is for. The difficulty in the proof occurs just after (19.7); we said that are finite at which is not true for.
However, the negative powers of x cancel if. Show this for by using two terms of the power series (12.9) or (13.1) for the function [see (13.3)].
Find the norm of each of the following functions on the given interval and state the normalized function.
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