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A new Stirling series as continued fraction. (English) Zbl 1213.33007

Summary: We have the well-known Stirling’s formula n!2πn(n e) n . This formula is the first approximation of the stirling series:

n2πnn e n exp(1 12n - 1 360n 3 + 1 1260 n 5 - ·

The author has formulated the following new Stirling series as a continued fraction

n!2πnn e n exp1 12n+2 5 n+53 210 n+195 371 n+22999 22737 n+


MSC:
33B15Gamma, beta and polygamma functions
11B73Bell and Stirling numbers
40A15Convergence and divergence of continued fractions
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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