1. The problem statement, all variables and given/known data 2. Relevant equations and in chapter 1 I believe that wanted me to note that 3. The attempt at a solution For the first part of this question, as a general statement, I know that P[2 n + 1](0) = 0 will be true as 2n+1 is an odd number, meaning that L is odd, and so the Legendre polynomial will be odd. With odd Legendre polynomials, every coefficient has a term of x attributed to it (example P3(x) = 1/2(5x^3 - 3x)), so if it were to be evaluated at 0, the result will always be zero. However I am not sure how to prove that using the Generating function. As for the second part of this question, I am not really sure what to do. For now I am looking for a place to start with that. [EDIT] I did expand 5.1 as a Maclaurin Series, but I don't see how they want me to equate that to 5.2.