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Question: 8 consider the legendre equatioa it ean be ahowa that...

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8. Consider the Legendre equatioa It ean be ahowa that one of the two limcarly independent series solutions of t Legendze equation becomes & polynomial of degree il n is equal to the integer t The Legendre polynonial of order 1, ic..(s), ік defined as the polynomial solution of the Legendre equation with a- that also sasiefies the condition P(l) 1. he It can be verifiod taas the Legendre polyzurmial of order f is given by the Rodriguee formula Namely, Polx)-1, P(, P( 1)/2, etc. Its known that the Legendre polyaomials setialy the follewing orkhogonalšty property: BLS (s) Determiue the radli of roovengeace nf the series solutions about 0 or the Legendre equation (b) A palytionaal of degree n, say f(s), dedued on the interval-1 I can be eoxpreseed as )P). Find the expausion coefficienls ce and show that ce vanjslu iff > 12. (c) Bxpand f 1 ia terms of the Lagendze polyiomials Pite) on the

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