Question

8.2.6

Given that Pn(x) = x and Q0(x) = 12ln(1+x1-x)$96EAAAAASUVORK5CYII=$ are solutions of Legendre’s differential equation (Table 7.1) corresponding to different eigenvalues. (a) Evaluate their orthogonality integral -11x2ln(1+x1-x)dx . (b) Explain why these two functions are not orthogonal, that is, why the proof of orthogonality does not apply.

It's in Mathematical Methods for Physicists 7e, Arfken ch8.2 Hermition operator

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Please explain as much as possible and solve it step by step.

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Given that 8.2.6 Pand Qncr)-n( are solutions of Legendre's differential equation (Table 7.1) corresponding to different eigenvalues Evaluate their orthogonality integral (a) b) Explain why these two functions are not orthogonal, that is, why the proof of orthogonality does not apply.

Answer 1

Link for integral calculation. Just type x/2ln((1+x)/(1-x)) and hit go.

https://www.integral-calculator.com/please rate

calcalated using sfa'- f-153 uSin I did it using edt online Hoo 6) Or thegenalisty hesern fate i is anly noa solutions oflegendhe Hio ac