A143306 - OEIS

%I #16 Jun 06 2021 07:32:44

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

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

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

%N Decimal expansion of the transcendental constant in the definition of van der Corput's constant (negated).

%C The unique solution c to the equation Integral_{x=0..sqrt(Pi/2-c)} sin(x^2 + c) dx in the range [-Pi/2, Pi/2]. - _Amiram Eldar_, Jun 06 2021

%H G. C. Greubel, <a href="/A143306/b143306.txt">Table of n, a(n) for n = 0..10000</a>

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

%e -0.72664324681324250959...

%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]; RealDigits[c0, 10, 105][[1]] (* _Jean-François Alcover_, Jul 16 2013, after _Eric W. Weisstein_ *)

%Y Cf. A143305.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Aug 05 2008