The Asymptotic Series for the Gamma Function is given by

(1) |

(2) |

The expansion of is what is usually called Stirling's series. It is given by the simple analytic expression

(3) | |||

(4) |

where is a Bernoulli Number.

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, p. 257, 1972.

Arfken, G. ``Stirling's Series.'' §10.3 in *Mathematical Methods for Physicists, 3rd ed.*
Orlando, FL: Academic Press, pp. 555-559, 1985.

Conway, J. H. and Guy, R. K. ``Stirling's Formula.'' In *The Book of Numbers.*
New York: Springer-Verlag, pp. 260-261, 1996.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York:
McGraw-Hill, p. 443, 1953.

Sloane, N. J. A. Sequences
A001163/M5400
and A001164/M4878
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26