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!)
A086280 Decimal expansion of 3rd Stieltjes constant gamma_3. 21
0, 0, 2, 0, 5, 3, 8, 3, 4, 4, 2, 0, 3, 0, 3, 3, 4, 5, 8, 6, 6, 1, 6, 0, 0, 4, 6, 5, 4, 2, 7, 5, 3, 3, 8, 4, 2, 8, 5, 7, 1, 5, 8, 0, 4, 4, 4, 5, 4, 1, 0, 6, 1, 8, 2, 4, 5, 4, 8, 1, 4, 8, 3, 3, 3, 6, 9, 1, 3, 8, 3, 4, 4, 9, 2, 1, 1, 2, 9, 7, 0, 0, 5, 3, 5, 7, 0, 5, 5, 7, 1, 6, 6, 2, 2, 8, 5, 6, 6, 7, 0, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 166.
LINKS
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint (2022). arXiv:2210.04609 [math.NT]
Eric Weisstein's World of Mathematics, Stieltjes Constants
FORMULA
Using the abbreviations a = log(z^2 + 1/4)/2, b = arctan(2*z) and c = cosh(Pi*z) then gamma_3 = -(Pi/4)*Integral_{0..infinity} (a^4 - 6*a^2*b^2+b^4)/c^2. gamma_4 = -(Pi/5)*Integral_{0..infinity} (a^5 - 10*a^3*b^2 + 5*a*b^4) / c^2. The general case is for n>=0 (which includes Euler's gamma as gamma_0) gamma_n = (-Pi/(n+1))* Integral_{0..infinity} sigma(n+1)/c^2, where sigma(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n,2*k)*b^(2*k)*a^(n-2*k). - Peter Luschny, Apr 19 2018
EXAMPLE
0.0020538...
MAPLE
evalf(gamma(3)) ; # R. J. Mathar, Feb 02 2011
MATHEMATICA
Join[{0, 0}, RealDigits[ N[ -StieltjesGamma[3], 103]][[1]]] (* Jean-François Alcover, Nov 07 2012 *)
CROSSREFS
Sequence in context: A095245 A324245 A173732 * A349950 A164976 A261745
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 14 2003
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 March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)