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%I #12 Aug 23 2024 03:52:33
%S 3,4,6,8,6,5,2,1,1,0,2,3,8,0,9,4,9,6,0,4,2,0,3,5,1,0,0,0,4,7,1,1,3,3,
%T 2,5,3,1,8,1,1,8,7,8,0,5,7,1,6,2,0,0,8,2,3,3,6,4,4,9,2,4,3,8,6,8,1,1,
%U 8,2,9
%N Decimal expansion of the Fresnel integral Integral_{x=0..oo} sin(x^4) dx.
%C Imaginary part associated with A206161.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fresnel_integral">Fresnel Integral</a>.
%F Equals A093954 * A182168 / A068465.
%F (this constant)^2 + A206161 ^2 = A068467 ^2.
%e 0.3468652110238094960420351000471...
%p evalf(Pi*sin(Pi/8)/GAMMA(3/4)/2^(3/2)) ;
%t RealDigits[Pi * Sin[Pi/8] / (2^(3/2) * Gamma[3/4]), 10, 120][[1]] (* _Amiram Eldar_, Aug 23 2024 *)
%Y Cf. A068465, A068467, A093954, A182168, A206161.
%K nonn,cons,easy
%O 0,1
%A _R. J. Mathar_, Jan 10 2013