%I #23 Jan 17 2020 05:28:19

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

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

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

%N Decimal expansion of Sierpiński's S^ (Ŝ or "S hat" as named by S. Finch), a constant appearing in the asymptotics of the number of representations of a positive integer as a sum of two squares.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.10 Sierpinski's constant, p. 122.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, Section 2.10 p. 17.

%F S_hat = gamma + S - 12/Pi^2*zeta'(2) + log(2)/3 - 1, where S = A086058 - 1 = A062089 / Pi.

%e 1.7710119609560939428739802335360529080166503945687208610228709...

%t S = 2* EulerGamma + 2*Log[2 ] + 3*Log[Pi] - 4* Log[Gamma[1/4]]; (* S^ *) Sh = EulerGamma + S - 12/Pi^2 Zeta'[2] + Log[2]/3 - 1; RealDigits[Sh, 10, 101] // First

%o (PARI) 3*Euler + 3*log(Pi) - 4*lngamma(1/4) - 12*zeta'(2)/Pi^2 + 7*log(2)/3 - 1 \\ _Charles R Greathouse IV_, Aug 08 2014

%Y Cf. A062089, A086058.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Aug 07 2014