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A086237 Decimal expansion of Porter's Constant. 2

%I

%S 1,4,6,7,0,7,8,0,7,9,4,3,3,9,7,5,4,7,2,8,9,7,7,9,8,4,8,4,7,0,7,2,2,9,

%T 9,5,3,4,4,9,9,0,3,3,2,2,4,1,4,8,8,7,7,7,7,3,9,9,6,8,5,8,1,7,6,1,6,6,

%U 0,6,7,4,4,3,2,9,0,4,4,8,0,8,4,3,0,3,6,9,3,2,7,5,1,1,1,7,4,0,1,5,2,1,2,6,6

%N Decimal expansion of Porter's Constant.

%C In his 'Addendum' to his paper in the year 2000 Don Knuth writes: "Gustav Lochs deserves to be mentioned here, because his work preceded that of Porter by nearly 15 years and involved essentially the same constant. Perhaps we should [..] refer in future to the Lochs-Porter constant, instead of simply saying 'Porter's constant'." - _Peter Luschny_, Aug 26 2014

%D S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 157

%D Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 113.

%H G. C. Greubel, <a href="/A086237/b086237.txt">Table of n, a(n) for n = 1..10000</a>

%H D. E. Knuth, <a href="http://dx.doi.org/10.1016/0898-1221(76)90025-0">Evaluation of Porter's constant</a>, Computers and Mathematics with Applications, 2 (1976), 137-139.

%H Gustav Lochs, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002473038&amp;IDDOC=247920">Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche</a>, Monatshefte für Mathematik, 65 (1961), 27-52.

%H J. W. Porter, <a href="http://dx.doi.org/10.1112/S0025579300004459">On a Theorem of Heilbronn</a>, Mathematika 22 1975, 20-28.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PortersConstant.html">Porter's Constant</a>

%F Equals 6*(log(2)/Pi^2)*(3*log(2) + 4*Gamma -(24/Pi^2)*Zeta'(2) - 2) - 1/2.

%e 1.4670780794339754728977984847072299534499033224149...

%t RealDigits[(6 Log[2] (48 Log[Glaisher] - Log[2] - 4 Log[Pi] - 2))/Pi^2 - 1/2, 10, 110][[1]] (* _Eric W. Weisstein_, Aug 22 2013 *)

%t RealDigits[(6 Log[2] (Pi^2 (-2 + 4 EulerGamma + Log[8]) - 24 Zeta'[2]))/Pi^4 - 1/2, 10, 110][[1]] (* _Eric W. Weisstein_, Aug 22 2013 *)

%o (PARI) x=.25^default(realprecision)

%o (6*log(2)*(4-48*(zeta(-1+x)-zeta(-1))/x-log(2)-4*log(Pi)-2))/Pi^2 - 1/2 \\ _Charles R Greathouse IV_, Aug 22 2013

%o (PARI) (6*log(2)*(4-48*zeta'(-1)-log(2)-4*log(Pi)-2))/Pi^2-1/2 \\ _Charles R Greathouse IV_, Dec 12 2013

%o (PARI) 6*log(2)/Pi^2*(3*log(2) + 4*Euler - 24/Pi^2*zeta'(2) - 2) - 1/2 \\ _Michel Marcus_, Aug 27 2014

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Jul 12 2003

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Last modified November 14 15:10 EST 2019. Contains 329126 sequences. (Running on oeis4.)