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Decimal expansion of the Fresnel Integral int_{x=0..infinity} x*cos(x^3) dx.
3

%I #12 Sep 08 2022 08:46:01

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

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

%U 7,1,6

%N Decimal expansion of the Fresnel Integral int_{x=0..infinity} x*cos(x^3) dx.

%H G. C. Greubel, <a href="/A205885/b205885.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fresnel_integral">Fresnel Integral</a>

%F Equals A073006/6.

%e 0.2256863232377334028242146713590856309...

%p evalf(GAMMA(2/3)/6) ;

%t RealDigits[Gamma[2/3]/6, 10, 100][[1]] (* _G. C. Greubel_, Dec 13 2017 *)

%o (PARI) gamma(2/3)/6 \\ _G. C. Greubel_, Dec 13 2017

%o (Magma) C<i> := ComplexField(); [Gamma(2/3)/6]; // _G. C. Greubel_, Dec 13 2017

%K nonn,cons,easy

%O 0,1

%A _R. J. Mathar_, Jan 10 2013