It is quite irresistible to play around with these formulae until one finds a simple expression that even Mma 9.0.0 can't simplify: try this: LerchPhi[1, 2*k, 1/2]/2^(2*k) /( -(-1)^k BernoulliB[2k] (2 Pi)^(2k)/(2k)!/2) == 1-1/2^(2k) or shorter: FullSimplify[LerchPhi[1, 2*k, 1/2]/2^(2*k)/Zeta[2 k]] just cute, no? Wouter -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Simon Plouffe Sent: woensdag 13 maart 2013 23:02 To: math-fun Subject: [math-fun] a certain formula of Euler, primes and Pi Hello, I have a friend in Moncton (NB, canada) a math professor, Paul Deguire, browsing around with the history of math and came accros this formula (well known ?) of pi : http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80 see the center of the page with prime numbers, also this one http://mathworld.wolfram.com/PiFormulas.html formulas 60 and 61. It deals with prime numbers , an infinite product and pi. Is there someone that knows a reference for this formula, when it was found by Euler ? Any information that would enlight this almost pi day, Best regards, Simon Plouffe _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.