login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086281 Decimal expansion of 4th Stieltjes constant gamma_4. 12
0, 0, 2, 3, 2, 5, 3, 7, 0, 0, 6, 5, 4, 6, 7, 3, 0, 0, 0, 5, 7, 4, 6, 8, 1, 7, 0, 1, 7, 7, 5, 2, 6, 0, 6, 8, 0, 0, 0, 9, 0, 4, 4, 6, 9, 4, 1, 3, 7, 8, 4, 8, 5, 0, 9, 9, 0, 7, 5, 8, 0, 4, 0, 9, 0, 7, 1, 2, 4, 8, 4, 1, 0, 0, 5, 3, 1, 5, 5, 2, 1, 9, 0, 0, 3, 0, 1, 6, 7, 8, 0, 5, 9, 0, 3, 9, 3, 0, 6, 3, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 166.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Stieltjes Constants

Wikipedia, Stieltjes constants

FORMULA

Using the abbreviations a = log(z^2 + 1/4)/2, b = arctan(2*z) and c = cosh(Pi*z) then 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

0.0023253...

MATHEMATICA

Join[{0, 0}, RealDigits[ N[ -StieltjesGamma[4], 103]][[1]]] (* Jean-Fran├žois Alcover, Nov 07 2012 *)

CROSSREFS

Cf. A001620, A082633, A086279, A086280, A086282, A183141, A183167, A183206, A184853, A184854.

Sequence in context: A285512 A232928 A026235 * A097975 A130088 A078834

Adjacent sequences:  A086278 A086279 A086280 * A086282 A086283 A086284

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 03:52 EST 2018. Contains 318141 sequences. (Running on oeis4.)