Unified approaches to the approximations of the gamma function (Q5964557)
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scientific article; zbMATH DE number 6547330
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unified approaches to the approximations of the gamma function |
scientific article; zbMATH DE number 6547330 |
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Unified approaches to the approximations of the gamma function (English)
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29 February 2016
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approximations
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gamma function
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Bell polynomials
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0.9319415
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0.9315787
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0.9149792
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0.91316473
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0.9015258
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0.90081716
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0.8990371
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0.89612097
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Based on the exponential complete Bell polynomials \(Y_n\) defined by NEWLINE\[NEWLINE\exp\Biggl(\sum^\infty_{m=1} x_m\cdot t^m/m!\Biggr)= \sum^\infty_{n=0} Y_n(x_1,\dots, x_n)\,t^n/n!,NEWLINE\]NEWLINE combined with Stirling's formula, the author obtains a new asymptotic approximation for the gamma function, unifying many earlier results in the literature (De Moivre, Gosper, Gosper-Smith, Laplace, Ramanujan, Batir, Chen, Nemes, etc.). Also, it is possible to obtain new approximations by this method.
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