27 May
2005
27 May
'05
10:33 a.m.
Well, cute anyway. I assume these aren't news to some of our readers. Rich -----Original Message----- From: Number Theory List [mailto:NMBRTHRY@LISTSERV.NODAK.EDU] On Behalf Of Troy Kessler Sent: Friday, May 27, 2005 6:46 AM To: NMBRTHRY@LISTSERV.NODAK.EDU Subject: Beautiful Zeta(3) formulas! 29/32 -3*Zeta[3]/4 = sum n=0 to oo (n)!^3/(n+3)!^3 (mathematica can do) 5*(-2077+1728Zeta[3])/1327104 = sum n=0 to oo (n)!^3/(n+5)!^3 Mathematica gives an answer that is 5 lines long for this second sum. It can be shown that if 3 or 5 is replaced with a odd number the result is rational + rational *Zeta[3]. (Use Zeilberger in A=B)