Legendre_Polynomial -210122121927
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The document discusses the Legendre polynomial and the Birch and Swinnerton-Dyer conjecture. It provides equations for the Riemann zeta function L(C,s) and a second order linear differential equation related to Legendre polynomials. It also gives expressions for the eigenvalues 了 and coefficients cn of the Legendre polynomial series expansion.
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Legendre_Polynomial -210122121927
- 1. The Legendre Polynomial Of The Birch and Swinnerton- Dyer Conjecture Gregory M. Prew 8/20/2015
- 2. L(C,s) = c(s-1)r s=1, r=2, & c0 = c(s-1)(s-1) = c(s2 -2s+1) (1-s2 )y卒卒(s) - 2sy卒(s) + 了 y(s) = 0 y1 = c0 + c2ks2k k=1 了 = n(n+1) = 2(2+1) = 6 cn = (2n)! 2n (n!)2 y1 = 1+ 3/2 (1)2 + 4.375 (1)4 ++cnsn