Abstract
IN connexion with the recent letters published in NATURE on Stirling's Theorem, I beg to say that in a paper accepted for publication by the Academy of Zagreb on July 13, and now in print, I proved in quite an elementary manner the formula Which coincides with the results published by Mr. James Henderson in NATURE of July 21, p. 97, formula (3) . The error was found to be of the order of 1/72 √3n2 of the calculated value, where 1/72 √3 is equal to 0.00801875 in Mr. Henderson's results. The formula may also be written and the log p determined once for all. (For a = 0.2113249, we have log p = 0.5244599.) The work of calculation is then by no means greater than in using Stirling's or Mr. H. E. Soper's formula though the approximation is far closer. I think the doubt inferred by Mr. G. J. Lidstone in NATURE of August 25, p. 283, on the usefulness of the formulæ under discussion is not valid so far as the present one is concerned. For sufficiently large values of n, depending on the number of decimals of the tables, the result calculated from the above formula is not worse than that furnished by any other more complicated formula.
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HONDL, S. Stirling's Theorem. Nature 112, 726 (1923). https://doi.org/10.1038/112726c0
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DOI: https://doi.org/10.1038/112726c0
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