%I #15 Jun 06 2021 05:26:24

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

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

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

%N Decimal expansion of van der Corput's constant.

%C Named after the Dutch mathematician Johannes Gaultherus van der Corput (1890-1975). - _Amiram Eldar_, Jun 06 2021

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 245-246.

%H G. C. Greubel, <a href="/A143305/b143305.txt">Table of n, a(n) for n = 1..10000</a>

%H J. G. van der Corput, <a href="https://doi.org/10.1007/BF01458693">Zahlentheoretische abschätzungen</a>, Mathematische Annalen, Vol. 84, No. 1 (1921), pp. 53-79; <a href="https://eudml.org/doc/158879">alternative link</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/vanderCorputsConstant.html">van der Corput's Constant</a>.

%F Equals 2*sqrt(2) * Integral_{x=0..sqrt(Pi/2-c)} cos(x^2 + c) dx, where c = A143306. - _Amiram Eldar_, Jun 06 2021

%e 3.3643175781558991060...

%t c0 = c /. FindRoot[ Cos[c]*FresnelS[Sqrt[1 - 2*c/Pi]] + FresnelC[Sqrt[1 - 2*c/Pi]]*Sin[c] == 0, {c, -1}, WorkingPrecision -> 110]; m = 2*Sqrt[Pi]*(Cos[c0]*FresnelC[Sqrt[1 - 2*c0/Pi]] - FresnelS[Sqrt[1 - 2*c0/Pi]]*Sin[c0] ) ; RealDigits[m, 10, 105][[1]] (* _Jean-François Alcover_, Jul 16 2013, after _Eric W. Weisstein_ *)

%Y Cf. A143306.

%K nonn,cons

%O 1,1

%A _Eric W. Weisstein_, Aug 05 2008