2018/04/14 by Robert M. Corless, Corless, Robert M., Leili Rafiee Sevyeri +1
Physics and Astronomy · #Experimental and Theoretical Physics Studies
paper · pdf · doi:10.48550/arxiv.1804.05263
We give an apparently new proof of Stirling's original asymptotic formula for\nthe behavior of \ln z! for large z. Stirling's original formula is not the\nformula widely known as "Stirling's formula", which was actually due to De\nMoivre. We also show by experiment that this old formula is quite effective for\nnumerical evaluation of \ln z! over \ℂ, when coupled with the\nsequence acceleration method known as Levin's u-transform. As an homage to\nStirling, who apparently used inverse symbolic computation to identify the\nconstant term in his formula, we do the same in our proof.\n