A204067 Decimal expansion of the Fresnel Integral, Integral_{x >= 0} cos(x^3) dx.

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, 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, 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

Offset: 0

Author

R. J. Mathar, Jan 10 2013

Keywords

• nonn
• cons
• easy

Examples

			0.7733429420779898501961016...
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..2000
• R. J. Mathar, Series expansion of generalized Fresnel integrals, arXiv:1211.3963 [math.CA], 2012, eq. (3.8).
• Wikipedia, Fresnel Integral.

Crossrefs

Cf. A010469, A019670, A073005, A073006, A204068, A217481.

Programs

Maple

evalf(int(cos(x^3),x=0..infinity),120); # Muniru A Asiru, Sep 26 2018

Mathematica

RealDigits[Gamma[1/3]/(2*Sqrt[3]), 10, 120][[1]] (* Amiram Eldar, May 26 2023 *)

PARI

Pi/(3*gamma(2/3)) \\ Gheorghe Coserea, Sep 26 2018

PARI

intnum(x=[0, -2/3], [oo, I], cos(x)/x^(2/3))/3 \\ Gheorghe Coserea, Sep 26 2018

Formula

Equals Pi/(3*Gamma(2/3)) = A019670 / A073006.

Equals Gamma(1/3)/(2*sqrt(3)) = A073005 / A010469. - Amiram Eldar, May 26 2023