

A086237


Decimal expansion of Porter's Constant.


1



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, 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, 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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 LochsPorter constant, instead of simply saying 'Porter's constant'."  Peter Luschny, Aug 26 2014


REFERENCES

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 157
Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 113.


LINKS

Table of n, a(n) for n=1..105.
D. E. Knuth, Evaluation of Porter's constant, Computers and Mathematics with Applications, 2 (1976), 137139.
Gustav Lochs, Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche, Monatshefte für Mathematik, 65 (1961), 2752.
J. W. Porter, On a Theorem of Heilbronn, Mathematika 22 1975, 2028.
Eric Weisstein's World of Mathematics, Porter's Constant


FORMULA

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


EXAMPLE

1.4670...


MATHEMATICA

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 *)
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 *)


PROG

(PARI) x=.25^default(realprecision)
(6*log(2)*(448*(zeta(1+x)zeta(1))/xlog(2)4*log(Pi)2))/Pi^2  1/2 \\ Charles R Greathouse IV, Aug 22 2013
(PARI) (6*log(2)*(448*zeta'(1)log(2)4*log(Pi)2))/Pi^21/2 \\ Charles R Greathouse IV, Dec 12 2013
(PARI) 6*log(2)/Pi^2*(3*log(2) + 4*Euler  24/Pi^2*zeta'(2)  2)  1/2 \\ Michel Marcus, Aug 27 2014


CROSSREFS

Sequence in context: A082237 A042976 A090142 * A200410 A136323 A135798
Adjacent sequences: A086234 A086235 A086236 * A086238 A086239 A086240


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Jul 12 2003


STATUS

approved



