8 Jan
2008
8 Jan
'08
6:38 a.m.
On 1/7/08, Eugene Salamin <gene_salamin@yahoo.com> wrote:
Do you have a proof for the value of u^{kk} ?
Cserti's paper equation (32) quotes a recurrence equivalent to (2*k+1) u^{k+!,k+1} - 2(2*k) u^{k,k} + (2*k-1) u^{k-1,k-1} = 0 from which u^{kk} = ( 1 + 1/3 + 1/5 + ... + 1/(2k-1) ) 2/\pi follows easily, given initial values u^{00} = 0, u^{11} = 2/\pi. He credits this to T. Morita, J. Math. Phys. 12, 1744–1747 (1971), but gives no proof. WFL