A157957 - OEIS

%I #26 Jun 17 2021 04:37:13

%S 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,

%T 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,

%U 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

%N Decimal expansion of the Littlewood-Salem-Izumi constant.

%C 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

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

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

%H J. Arias de Reyna and J. van de Lune, <a href="http://dx.doi.org/10.1090/S0025-5718-09-02222-4">High precision computation of a constant in the theory of trigonometric series</a>, Math. Comp., Vol. 78, No. 268 (2009), pp. 2187-2191.

%H R. P. Boas and V. C. Klema, <a href="http://dx.doi.org/10.1090/S0025-5718-1964-0176283-9">A constant in the theory of trigonometric series</a>, Math. Comp., Vol. 18, No. 88 (1964), p. 674. [Gives incorrect digits]

%H Robert F. Church, <a href="http://dx.doi.org/10.1090/S0025-5718-65-99245-8">On a constant in the theory of trigonometric series</a>, Math. Comp., Vol. 19, No. 91 (1965), p. 501.

%H Karl Grandjot, Vojtěch Jarnik, Edmund Landau and John Edensor Littlewood, <a href="http://dx.doi.org/10.1007/BF02410076">Bestimmung einer absoluten Konstanten aus der Theorie der trigonometrischen Reihen</a>, Annali di Mat., Vol. 6, No. 1 (1929), pp. 1-7.

%H Yudell L. Luke, Wyman Fair, Geraldine Coombs and Rosemary Moran, <a href="http://dx.doi.org/10.1090/S0025-5718-65-99246-X">On a constant in the theory of trigonometric series</a>, Math. Comp., Vol. 19, No. 91 (1965), pp. 501-502.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Littlewood-Salem-IzumiConstant.html">Littlewood-Salem-Izumi Constant</a>.

%e 0.30844377956198600303...

%t 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_ *)

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

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Mar 10 2009