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 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. 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)