The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A097303 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A097303

Denominators in Stirling's asymptotic series.
(history; published version)

#15 by Alois P. Heinz at Fri Sep 23 17:20:13 EDT 2022

STATUS

proposed

approved

#14 by Jon E. Schoenfield at Fri Sep 23 17:15:37 EDT 2022

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Fri Sep 23 17:15:34 EDT 2022

COMMENTS

Stirling's formula for GAMMAGamma(z) (|arg(z)| < Pi) uses the asymptotic series sum(Sum_{k>=0} (N(k)/a(k))*((1/z)^k)/k!,k=0..infinity). For N(k) see the W. Lang link.

FORMULA

a(n) = denominator(s(n)), where the signed rationals s(n) are the coefficients of ((1/z)^k)/k! in the asymptotic series appearing in Stirling's formula for GAMMAGamma(z).

STATUS

approved

editing

#12 by Wolfdieter Lang at Fri Aug 30 03:32:02 EDT 2019

STATUS

editing

approved

#11 by Wolfdieter Lang at Fri Aug 30 03:31:59 EDT 2019

LINKS

W. Lang, <a href="/LANGCHANGE/A097303/a097303.texttxt">More terms and comments</a>.

STATUS

approved

editing

#10 by N. J. A. Sloane at Wed Aug 28 09:25:23 EDT 2019

LINKS

W. Lang, <a href="http://www.itp.kit.edu/~wl/EISpubLANGCHANGE/A097303.text">More terms and comments</a>.

Discussion

Wed Aug 28

09:25

OEIS Server: https://oeis.org/edit/global/2824

#9 by Charles R Greathouse IV at Thu Jul 09 17:57:08 EDT 2015

LINKS

W. Lang, <a href="http://www-.itp.physik.uni-karlsruhekit.deedu/~wl/EISpub/A097303.text">More terms and comments</a>.

Discussion

Thu Jul 09

17:57

OEIS Server: https://oeis.org/edit/global/2449

#8 by Charles R Greathouse IV at Thu Nov 21 13:11:41 EST 2013

MATHEMATICA

max = 15; se = Series[(E^x*Sqrt[1/x]*Gamma[x+1])/(x^x*Sqrt[2*Pi]), {x, Infinity, max}]; Denominator[ CoefficientList[ se /. x -> 1/x, x]*Range[0, max]!] (* From _Jean-François Alcover, _, Nov 03 2011 *)

Discussion

Thu Nov 21

13:11

OEIS Server: https://oeis.org/edit/global/2066

#7 by R. J. Mathar at Mon Jul 23 09:33:56 EDT 2012

STATUS

editing

approved

#6 by R. J. Mathar at Mon Jul 23 09:33:51 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 13 2004

Wolfdieter Lang, Aug 13 2004

STATUS

approved

editing