login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 Lochs-Porter 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), 137-139.

Gustav Lochs, Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche, Monatshefte für Mathematik, 65 (1961), 27-52.

J. W. Porter, On a Theorem of Heilbronn, Mathematika 22 1975, 20-28.

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)*(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

(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

(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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified October 21 02:48 EDT 2014. Contains 248371 sequences.