And, by definition, for f(x) = 2^-x, S is the transcendental Prouhet-Thue-Morse constant: http://en.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant
Sent: Monday, July 07, 2014 at 12:29 AM From: "Warren D Smith" <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Some Wilsonian sums
h(n) = (-1)^(parity of bit-sum of binary representation of n)
f(x) S=SUM[ f(n) * h(n), for n=0..2^k-1 with k large] ln(x+1) S=-log(2)/2 ln(x+2) S = -0.1379330125 ln(x+3) -0.07070756527 x^j 0 for any fixed integer j>=0 1/(x+1) 0.398761088108 1/(x+2) 0.1049709156499 sqrt(x) -0.63407426 1/sqrt(x+1) 0.1983140804979
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