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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

6*ln2/Pi^2 (3*ln2 + 4 Gamma - 24/Pi^2*Zeta'(2) - 2)

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.

Eric Weisstein's World of Mathematics, Porter's Constant

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

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

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Last modified July 29 02:13 EDT 2014. Contains 245013 sequences.