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A157957
Decimal expansion of the Littlewood-Salem-Izumi constant.
0
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
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Mar 10 2009
STATUS
approved