Asymptotic approximations for n!

Richard B. Paris

Asymptotic approximations for n!

Richard B. Paris

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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Abstract

Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.

Original language	English
Pages (from-to)	1801-1807
Number of pages	7
Journal	Applied Mathematical Sciences
Volume	5
Issue number	37-40
Publication status	Published - 2011

Keywords

Factorial function
Asymptotic expansion
Approximations

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Cite this

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title = "Asymptotic approximations for n!",

abstract = "Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling{\textquoteright}s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.",

author = "Paris, \{Richard B.\}",

year = "2011",

language = "English",

volume = "5",

pages = "1801--1807",

journal = "Applied Mathematical Sciences",

issn = "1314-7552",

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AU - Paris, Richard B.

PY - 2011

Y1 - 2011

N2 - Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.

AB - Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.

M3 - Article

SN - 1314-7552

VL - 5

SP - 1801

EP - 1807

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

IS - 37-40

ER -

Asymptotic approximations for n!

Abstract

Keywords

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