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Legender's Equation-Mathematical Physics-Assignment, Exercises of Mathematical Physics

Central University of OrissaMathematical Physics

This assignment is for Mathematical Physics course. It was assigned by Dr. Akshat Nair at Central University of Odisha. It includes: Legendre, Equation, Converges, Spherical, Harmonics, Polynomial, Norm, Series, Generating, Function

Typology: Exercises

2011/2012

Uploaded on 07/19/2012

madan
madan 🇮🇳

11 documents

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/ Mathematical Physics Assignment Number 4. PAM -507 (Due on September 16, 2009) phage h Ae Question 1. ‘a Prove that | (a) P,(-1) — (-1)" \P) = j ie + % ts (b) P,(1)= 1 ee | D° 35 thy po! 3 (©) (2?) SM +] i j , dine - 6 yt? Question 3 ” “re Find the spherical harmonics Y;" (Cos8) for l=0, 1, 2, 3 “Question 4 Expand each of the following polynomials in Legendre’s series (a) 3x* +x -1 (b) 7x* -3 xt] ‘Question 5 Find the norm of Legendre’s polynomial using the generating function (x, h) for Legendre’s polynomial. Question 6 The generating function for Legendre’s polynomial is given as (x, h) = 3° Pi(xyh' i=0 Show that P;(x) is the solution of the Legendgre’s differential equation. docsity.com