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 A260230 Decimal expansion of S(Pi), where S(x) is the series Sum_{n>=1} (-1)^(n+1)*coth(n*x)/n. 0
 6, 9, 6, 8, 8, 5, 5, 7, 0, 7, 3, 8, 2, 8, 5, 2, 0, 0, 4, 3, 1, 4, 1, 5, 2, 6, 0, 9, 1, 1, 1, 2, 7, 9, 5, 6, 0, 5, 1, 7, 3, 6, 6, 0, 0, 1, 5, 2, 5, 8, 1, 4, 5, 0, 3, 5, 9, 3, 2, 7, 4, 3, 4, 4, 2, 4, 6, 5, 1, 1, 3, 9, 8, 7, 3, 4, 5, 8, 5, 1, 2, 0, 0, 6, 1, 3, 8, 3, 0, 2, 6, 3, 9, 4, 5, 7, 5, 1, 6, 5, 4, 9, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Vaclav Kotesovec, Jul 21 2015: (Start) Sum_{n>=1} (-1)^(n+1)*cos(n*x)/n = log(2*(1+cos(x)))/2. Sum_{n>=1} cos(n*x)/n = -log(2*(1-cos(x)))/2. (End) LINKS A. Dieckmann, Collection of Infinite Products and Series Jonathan D. Weiss, The Summation of One Class of Infinite Series, Applied Mathematics, 2014, 5, 2816-2822. Eric Weisstein's MathWorld, Inverse Nome FORMULA S(Pi) = Sum_{n>=1} (-1)^(n+1)*coth(n*Pi)/n = log(2) + 2*Sum_{k>=1} log(1+exp(-2*k*Pi)). Equals Pi/6 + (1/4)*log(2). EXAMPLE 0.69688557073828520043141526091112795605173660015258145035932743442465... MATHEMATICA RealDigits[Pi/6 + (1/4)*Log[2], 10, 104] // First CROSSREFS Sequence in context: A198144 A154394 A126599 * A159691 A118947 A023410 Adjacent sequences:  A260227 A260228 A260229 * A260231 A260232 A260233 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jul 20 2015 STATUS approved

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Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)