The "equivalent conjecture" was easy, once you know that, for m>1 K(m) conveniently falls into rectangular form: K(1/m)/sqrt(m) - i K(1-m) . So are these Fourier series really new? They seem too useful to be this obscure. Although the last one's a bit scummy. --rwg On Sat, Dec 4, 2010 at 9:48 PM, Bill Gosper <billgosper@gmail.com> wrote:

Better tested and less fishily written, they still look like closed forms for the Fourier coefficients of am, dn, and sc: http://gosper.org/fourndulum.pdf Familiar? --rwg