A143306 Decimal expansion of the transcendental constant in the definition of van der Corput's constant (negated).

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, 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, 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

Offset

0,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, van der Corput's Constant.

Example

-0.72664324681324250959...

Mathematica

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 *)

Crossrefs

Cf. A143305.

Sequence in context: A295874 A182548 A322933 * A199075 A228045 A011361

Adjacent sequences: A143303 A143304 A143305 * A143307 A143308 A143309

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 05 2008

Status

approved