A157957 Decimal expansion of the Littlewood-Salem-Izumi constant.

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

Offset

0,1

Comments

Named by Arias de Reyna and van de Lune (2009) after the British mathematician John Edensor Littlewood (1885-1977), the Greek mathematician Raphaël Salem (1898-1963) and the Japanese mathematician Shin-ichi Izumi (1904-1990). - Amiram Eldar, Jun 17 2021

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.14 Young-Fejér-Jackson constants, p. 244.

Antoni Zygmund, Trigonometric Series, Cambridge University Press, 1988, p. 379.

Links

Table of n, a(n) for n=0..104.

J. Arias de Reyna and J. van de Lune, High precision computation of a constant in the theory of trigonometric series, Math. Comp., Vol. 78, No. 268 (2009), pp. 2187-2191.

R. P. Boas and V. C. Klema, A constant in the theory of trigonometric series, Math. Comp., Vol. 18, No. 88 (1964), p. 674. [Gives incorrect digits]

Robert F. Church, On a constant in the theory of trigonometric series, Math. Comp., Vol. 19, No. 91 (1965), p. 501.

Karl Grandjot, Vojtěch Jarnik, Edmund Landau and John Edensor Littlewood, Bestimmung einer absoluten Konstanten aus der Theorie der trigonometrischen Reihen, Annali di Mat., Vol. 6, No. 1 (1929), pp. 1-7.

Yudell L. Luke, Wyman Fair, Geraldine Coombs and Rosemary Moran, On a constant in the theory of trigonometric series, Math. Comp., Vol. 19, No. 91 (1965), pp. 501-502.

Eric Weisstein's World of Mathematics, Littlewood-Salem-Izumi Constant.

Example

0.30844377956198600303...

Mathematica

x /. FindRoot[ HypergeometricPFQ[{1/2 - x/2}, {1/2, 3/2 - x/2}, -9*Pi^2/16] == 0, {x, 1/2}, WorkingPrecision -> 105] // RealDigits // First (* Jean-François Alcover, Oct 22 2012, after Eric W. Weisstein *)

Prog

(PARI) 1-solve(x=.6, .7, intnum(u=0, 3*Pi/2, u^x*sin(u))) \\ Charles R Greathouse IV, Mar 29 2012

Crossrefs

Sequence in context: A359258 A244854 A144807 * A201577 A375247 A223854

Adjacent sequences: A157954 A157955 A157956 * A157958 A157959 A157960

Keyword

nonn,cons

Author

Eric W. Weisstein, Mar 10 2009

Status

approved