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Legender's Polynomial-Mathematical Physics-Assignment, Exercises of Mathematical Physics
This assignment is for Mathematical Physics course. It was assigned by Dr. Akshat Nair at Central University of Odisha. It includes: Legendre, Polynomial, Orthogonally, Associated, Differential, Equation, Frobenius, Method, Plot, Function
Typology: Exercises
2011/2012
1 / 1
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, Question 7 Prove orthogonality of Associated Legendre Polynomial. ‘Question & Derive the solution of the radial part of the Legendre Differential] equation using Frobenius method. Question 9 Plot Legendre function of 1° kind Po(x), Pi(x), Pa(x), P3(x) on the same graph. Alos plot the Legendre function of 2™ kind Qo(x), Q(x), Qo(x) and Q3(x) on one graph. J dq em) x wry, (ne 4 ait ti 10 Sate I tet, TM S34 fh Question (EO Show that y(x) = u(x) (1-x*)™ * is the solution of the Associated Legendre’s equation (1-x°) y"(x) -2xy/ (XL mnt) ~ m(1-x2) Jy (%) =0 and satisfy the equation (1-x*) u(x) - 2(m+1) xu’ (x)+ [ n(nt+1)—m (m+1) ] u(x) =0 7 ( +7 YA 2 emt “ yp | | docsity.com