A097666 - OEIS

%I #22 Sep 08 2022 08:45:14

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

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

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

%N Decimal expansion of the constant 4*exp(psi(3/4) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

%C This constant appears in _Benoit Cloitre_'s generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-4 linear recursions with varying coefficients (see A097679 for example).

%D A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.

%H G. C. Greubel, <a href="/A097666/b097666.txt">Table of n, a(n) for n = 1..2500</a>

%H Benoit Cloitre, <a href="/A097679/a097679.pdf">On a generalization of Euler-Gauss formula for the Gamma function</a>, preprint 2004.

%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma Function</a>.

%H Andrew Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf">Asymptotic enumeration methods</a>, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.

%F c = 1/2*exp(Pi/2).

%e c = 2.40523869048267582773651783335191656319508543733226747001040...

%t RealDigits[1/2*E^(Pi/2), 10, 105][[1]] (* _Robert G. Wilson v_, Aug 27 2004 *)

%o (PARI) 4*exp(psi(3/4)+Euler)

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(Pi(R)/2)/2; // _G. C. Greubel_, Sep 07 2018

%Y Cf. A097663-A097665, A097667-A097676.

%K cons,nonn

%O 1,1

%A _Paul D. Hanna_, Aug 25 2004

%E More terms from _Robert G. Wilson v_, Aug 27 2004