A204068 Decimal expansion of the Fresnel Integral Integral_{x>=0} sin(x^3) dx.

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, 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, 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

Offset

0,1

Comments

Imaginary part associated with A204067.

Links

Table of n, a(n) for n=0..104.

R. J. Mathar, Series expansion of generalized Fresnel integrals, arXiv:1211.3963 [math.CA], 2012, eq. (3.8).

Wikipedia, Fresnel Integral.

Formula

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

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

Equals Gamma(1/3)/6 = A073005 / 6. - Amiram Eldar, May 26 2023

Example

0.446489755784624605609282...

Maple

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

Mathematica

RealDigits[Gamma[1/3]/6, 10, 120][[1]] (* Amiram Eldar, May 26 2023 *)

Crossrefs

Cf. A073005, A073010, A073006, A202623, A204067

Sequence in context: A255014 A131089 A256486 * A066560 A205031 A339719

Adjacent sequences: A204065 A204066 A204067 * A204069 A204070 A204071

Keyword

nonn,cons,easy

Author

R. J. Mathar, Jan 10 2013

Status

approved