A143305 Decimal expansion of van der Corput's constant.

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, 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, 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

Offset

1,1

Comments

Named after the Dutch mathematician Johannes Gaultherus van der Corput (1890-1975). - Amiram Eldar, Jun 06 2021

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

J. G. van der Corput, Zahlentheoretische abschätzungen, Mathematische Annalen, Vol. 84, No. 1 (1921), pp. 53-79; alternative link.

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

Formula

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

Example

3.3643175781558991060...

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]; 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 *)

Crossrefs

Cf. A143306.

Sequence in context: A278663 A086492 A372036 * A051472 A257957 A369501

Adjacent sequences: A143302 A143303 A143304 * A143306 A143307 A143308

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 05 2008

Status

approved