The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A075700 Decimal expansion of -zeta'(0). 37
 9, 1, 8, 9, 3, 8, 5, 3, 3, 2, 0, 4, 6, 7, 2, 7, 4, 1, 7, 8, 0, 3, 2, 9, 7, 3, 6, 4, 0, 5, 6, 1, 7, 6, 3, 9, 8, 6, 1, 3, 9, 7, 4, 7, 3, 6, 3, 7, 7, 8, 3, 4, 1, 2, 8, 1, 7, 1, 5, 1, 5, 4, 0, 4, 8, 2, 7, 6, 5, 6, 9, 5, 9, 2, 7, 2, 6, 0, 3, 9, 7, 6, 9, 4, 7, 4, 3, 2, 9, 8, 6, 3, 5, 9, 5, 4, 1, 9, 7, 6, 2, 2, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The probability density function for the standard normal distribution is e^(-x^2/2 + zeta'(0)). - Rick L. Shepherd, Mar 08 2014 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula. Eric Weisstein's World of Mathematics, Log Gamma Function. Eric Weisstein's World of Mathematics, Stirling's Approximation. Wikipedia, Gamma function. Wikipedia, Normal curve FORMULA Equals log(2*Pi)/2 = A061444/2 = log(A019727). Equals Integral_{x=0..1} log(Gamma(x)) dx. - Jean-François Alcover, Apr 29 2013 More generally, equals t-t*log(t)+Integral_{x=t..(t+1)} (log(Gamma(x)) dx for any t>=0 (the Raabe formula). - Stanislav Sykora, May 14 2015 Equals lim_{k->oo} log(k!) + k - (k + 1/2)*log(k) (by Stirling's formula). - Amiram Eldar, Aug 21 2020 EXAMPLE 0.91893853320467274178032... MAPLE evalf(log(2*Pi)/2, 120); # Muniru A Asiru, Oct 08 2018 MATHEMATICA Log[Sqrt[2*Pi]] // RealDigits[#, 10, 104] & // First (* Jean-François Alcover, Apr 29 2013 *) PROG (PARI) -zeta'(0) \\ Charles R Greathouse IV, Mar 28 2012 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Log(2*Pi(R))/2; // G. C. Greubel, Oct 07 2018 CROSSREFS Cf. A019727, A061444, A257549. Sequence in context: A299622 A163899 A198758 * A021843 A231931 A175615 Adjacent sequences:  A075697 A075698 A075699 * A075701 A075702 A075703 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Oct 02 2002 EXTENSIONS Normalized representation (leading zero and offset) R. J. Mathar, Jan 25 2009 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.

Last modified January 28 03:36 EST 2021. Contains 340490 sequences. (Running on oeis4.)