%I #27 Jun 28 2023 10:42:37
%S 7,7,3,3,4,2,9,4,2,0,7,7,9,8,9,8,5,0,1,9,6,1,0,1,6,1,1,2,9,5,2,1,7,3,
%T 4,0,9,2,4,8,0,6,8,4,7,2,2,4,2,1,5,6,7,2,6,6,2,0,3,1,9,5,5,4,7,2,9,7,
%U 6,5,7,1,1,6,1,1,6,0,6,4,6,6,5,0,3,8,6,4,9,5,7,5,9,9,9,6,0
%N Decimal expansion of the Fresnel Integral, Integral_{x >= 0} cos(x^3) dx.
%H Muniru A Asiru, <a href="/A204067/b204067.txt">Table of n, a(n) for n = 0..2000</a>
%H R. J. Mathar, <a href="http://arxiv.org/abs/1211.3963">Series expansion of generalized Fresnel integrals</a>, arXiv:1211.3963 [math.CA], 2012, eq. (3.8).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fresnel_integral">Fresnel Integral</a>.
%F Equals Pi/(3*Gamma(2/3)) = A019670 / A073006.
%F Equals Gamma(1/3)/(2*sqrt(3)) = A073005 / A010469. - _Amiram Eldar_, May 26 2023
%e 0.7733429420779898501961016...
%p evalf(int(cos(x^3),x=0..infinity),120); # _Muniru A Asiru_, Sep 26 2018
%t RealDigits[Gamma[1/3]/(2*Sqrt[3]), 10, 120][[1]] (* _Amiram Eldar_, May 26 2023 *)
%o (PARI) Pi/(3*gamma(2/3)) \\ _Gheorghe Coserea_, Sep 26 2018
%o (PARI) intnum(x=[0, -2/3], [oo, I], cos(x)/x^(2/3))/3 \\ _Gheorghe Coserea_, Sep 26 2018
%Y Cf. A010469, A019670, A073005, A073006, A204068, A217481.
%K nonn,cons,easy
%O 0,1
%A _R. J. Mathar_, Jan 10 2013