A204068 - OEIS

%I #16 May 26 2023 05:45:01

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

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

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

%N Decimal expansion of the Fresnel Integral Integral_{x>=0} sin(x^3) dx.

%C Imaginary part associated with A204067.

%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/(Gamma(2/3)* 3^(3/2)) = A073010 / A073006.

%F (this value)^2 + A204067^2 = A202623^2.

%F Equals Gamma(1/3)/6 = A073005 / 6. - _Amiram Eldar_, May 26 2023

%e 0.446489755784624605609282...

%p evalf(Pi/GAMMA(2/3)/3^(3/2) ) ;

%t RealDigits[Gamma[1/3]/6, 10, 120][[1]] (* _Amiram Eldar_, May 26 2023 *)

%Y Cf. A073005, A073010, A073006, A202623, A204067

%K nonn,cons,easy

%O 0,1

%A _R. J. Mathar_, Jan 10 2013