The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A245975 A188737 A200680 * A350763 A341318 A332324
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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