use the method of reduction of order and the known solution P_1(x) of Legendre\'

Question

use the method of reduction of order and the known solution P_1(x) of Legendre's equation to find the second solution Q_1(x) (in terms of an integral). Evaluate the integral for the cases l=0 and l=1 to find Q_0 and Q_1. Note the divergence of the logarithms at x= (+/-) 1. Expand the logarithms in Q_0 to get the divergent series mentioned above. [a_1 series in (2.7) with l=0, x^2=1]


do they want us to derive it from Legendre's equation for P_1(x) which is x and the reduction of order method? Again, not sure.....

Explanation / Answer

logarithms at x= (+/-) 1

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