A Convergent Version of Stirling's Formula
Thomas Bayes showed, in a letter to John Canton published by the Royal Society in 1763, that Stirling's formula did not give a convergent series.
Obtaining a convergent version of Stirling's formula entails evaluating
One way to do this is by means of a convergent series of inverted rising exponentials. If
where s(n, k) denotes the Stirling numbers of the first kind. From this we obtain a version of Stirling's series
which converges when Re(z) > 0.
Read more about this topic: Stirling's Theorem
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