A260129 Decimal expansion of the constant c_0 appearing in the asymptotic evaluation of the n-th Lebesgue constant (related to Fourier series) as L_n ~ (4/Pi^2)*log(n) + c_0.

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

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.2 Lebesgue constants, p. 251.

Links

Table of n, a(n) for n=1..103.

Leopold Fejér, Lebesguesche Konstanten und divergente Fourierreihen, Journal für die reine und angewandte Mathematik, Vol. 138 (1910), page 30.

Eric Weisstein's MathWorld, Lebesgue constants

Formula

c_0 = 2*Integral_{0..1} cos(Pi*t)*LogGamma(t) dt + 4*log(4/Pi)/Pi^2.

Also equals A243277 + log(16)/Pi^2 or (4/Pi^2)*(A243278 + log(2)).

Example

c_0 = 1.270353244921878457377403207006854753455707535864161213793859945557371...
Integral_{0..1} cos(Pi*t)*LogGamma(t) dt =
0.58622542534024658158560382093726746382526606396195055488919749303076...

Mathematica

c0 = 2*NIntegrate[Cos[Pi*t]*LogGamma[t], {t, 0, 1}, WorkingPrecision -> 103] + 4*Log[4/Pi]/Pi^2 ; RealDigits[c0] // First

Crossrefs

Cf. A157165, A157166, A157167, A157168, A226654, A226655, A226656, A243277, A243278.

Sequence in context: A245975 A188737 A200680 * A350763 A341318 A332324

Adjacent sequences: A260126 A260127 A260128 * A260130 A260131 A260132

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 17 2015

Status

approved