On Mon, Mar 25, 2013 at 6:14 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:
What does [RIES] have to say about zeta functions of odd integers?
-- Gene
I tried zeta(3) a couple years ago, just for fun. But the Zeta functions have been studied so well, I doubt RIES would have much to say. It explores a space defined by the union of Liouvillian numbers [1] and Chow's concept of "closed-form numbers" [1]. The only functions it has at present are the "field operations" (addition, subtraction, multiplication, division), exponentiation and logarithms, and the trig functions; and it can find implicit solutions like x-cos(pi*x)=1 or x^x-7=0. If the Zeta function were added, then of course RIES would just say 1.202057 is close to zeta(3). I doubt even all the special functions (Bessel, elliptic integral, hypergeometric, etc.) would help since presumably a lot of powerful minds have already looked at it. [1] See http://mathworld.wolfram.com/LiouvillianNumber.html [2] http://arxiv.org/abs/math/9805045v1 -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com