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A075700 Decimal expansion of -zeta'(0). 35
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

Table of n, a(n) for n=0..103.

J. Sondow and E. W. Weisstein, MathWorld: Wallis Formula

Eric Weisstein's World of Mathematics, Log Gamma Function

Wikipedia, Gamma function

Wikipedia, Normal curve

Index entries for zeta function.

FORMULA

zeta'(0) = -log(2*Pi)/2 = -A061444/2 = -log(A019727).

Also integral_{x=0..1} log(Gamma(x)). [Jean-François Alcover, Apr 29 2013]

More generally, equals t-t*log(t)+integral_{x=t..(t+1)} (log(Gamma(x)) for any t>=0 (the Raabe formula). - Stanislav Sykora, May 14 2015

EXAMPLE

0.91893853320467274178032...

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

CROSSREFS

Cf. A061444, A257549.

Sequence in context: A238168 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

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Last modified December 8 22:51 EST 2016. Contains 278957 sequences.