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A099289
Decimal expansion of the Fresnel sine integral function at 1.
1
4, 3, 8, 2, 5, 9, 1, 4, 7, 3, 9, 0, 3, 5, 4, 7, 6, 6, 0, 7, 6, 7, 5, 6, 6, 9, 6, 6, 2, 5, 1, 5, 2, 6, 3, 7, 4, 9, 3, 7, 8, 6, 5, 7, 2, 4, 5, 2, 4, 1, 6, 5, 6, 7, 3, 3, 4, 4, 0, 7, 3, 2, 6, 2, 6, 5, 8, 0, 5, 9, 3, 8, 2, 1, 1, 2, 9, 9, 8, 7, 7, 1, 7, 3, 4, 6, 0, 6, 7, 4, 1, 4, 1, 1, 5, 4, 8, 4, 5, 6, 7, 8, 7, 8, 3
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Fresnel Integrals.
Wikipedia, Fresnel integral.
FORMULA
From Amiram Eldar, Feb 06 2022: (Start)
Equals Integral_{x=0..1} sin(Pi*x^2/2) dx.
Equals Sum_{k>=0} (-1)^k * (Pi/2)^(2*k+1)/A003031(k). (End)
EXAMPLE
0.4382591473903547660767566966251526374937865724524165673344073262658...
MATHEMATICA
RealDigits[ FresnelS[1], 10, 105][[1]]
PROG
(PARI) intnum(x=0, 1, sin(Pi*x^2/2)) \\ Michel Marcus, Feb 06 2022
CROSSREFS
Sequence in context: A345133 A016703 A236266 * A231892 A065628 A077589
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Oct 11 2004
STATUS
approved