consapp_gamma.bib

@Inbook{Koepf2014,
author={{Koepf, W.}},
title="The Gamma Function",
bookTitle="Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities",
year="2014",
publisher="Springer",
address="London",
pages="1--10",
abstract="Apart from the elementary transcendental functions such as the exponential and trigonometric functions and their inverses, the Gamma function is probably the most important transcendental function. It was defined by Euler to interpolate the factorials at noninteger arguments.",
isbn="978-1-4471-6464-7",
doi="10.1007/978-1-4471-6464-7_1",
url="https://doi.org/10.1007/978-1-4471-6464-7_1"
}
@Inbook{Magnus1966a,
author={{Magnus, W., Oberhettinger, F., & Soni, R. P.}},
title="The gamma function and related functions",
bookTitle="Formulas and Theorems for the Special Functions of Mathematical Physics",
year="1966",
publisher="Springer",
address="Berlin, Heidelberg",
pages="1--37",
abstract="The function $\Gamma$(z) is a meromorphic function of z with simple poles at z = −n, (n = 0, 1, 2,...) with the respective residue {\$}{\$}{\backslash}frac{\{}{\{}{\{}{\{}( - 1){\}}^n{\}}{\}}{\}}{\{}{\{}n!{\}}{\}}.{\$}{\$}.",
isbn="978-3-662-11761-3",
doi="10.1007/978-3-662-11761-3_1",
url="https://doi.org/10.1007/978-3-662-11761-3_1"
}
@article{BATIR2008187,
title = {On some properties of the gamma function},
journal = {Expositiones Mathematicae},
volume = {26},
number = {2},
pages = {187-196},
year = {2008},
issn = {0723-0869},
doi = {10.1016/j.exmath.2007.10.001},
url = {https://www.sciencedirect.com/science/article/pii/S0723086907000497},
author = {{Batir, N.}},
keywords = {Gamma function, Digamma function, Polygamma functions, Complete monotonicity, Riemann zeta-function},
abstract = {In this paper we prove a complete monotonicity theorem and establish some upper and lower bounds for the gamma function in terms of digamma and polygamma functions.}
}
@article{5bcebaa1-7494-336c-85e9-de3c540e9f64,
 ISSN = {0003486X, 19398980},
 URL = {http://www.jstor.org/stable/1968254},
 author = {{Rasch, G.}},
 journal = {Annals of Mathematics},
 number = {3},
 pages = {591--599},
 publisher = {[Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University]},
 title = {Notes on the Gamma-Function},
 urldate = {2026-01-12},
 volume = {32},
 year = {1931}
}
@article{6b95b756-79df-32e7-8452-988d85f07718,
 ISSN = {0003486X, 19398980},
 URL = {http://www.jstor.org/stable/1967180},
 author = {{Gronwall, T. H.}},
 journal = {Annals of Mathematics},
 number = {2},
 pages = {35--124},
 publisher = {[Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University]},
 title = {The Gamma Function in the Integral Calculus},
 urldate = {2026-01-12},
 volume = {20},
 year = {1918}
}
@article{7c7965cf-2aff-3860-a01c-d57527fbdc42,
 ISSN = {00029890, 19300972},
 URL = {https://www.jstor.org/stable/48663320},
 abstract = {Since its inception in 1894, the Monthly has printed 50 articles on the Γ function or Stirling’s asymptotic formula, including the magisterial 1959 paper by Phillip J. Davis, which won the 1963 Chauvenet prize, and the eye-opening 2000 paper by the Fields medalist Manjul Bhargava. In this article, we look back and comment on what has been said, and why, and try to guess what will be said about the Γ function in future Monthly issues. We also identify some gaps, which surprised us: phase plots, Riemann surfaces, and the functional inverse of Γ make their first appearance in the Monthly here. We also give a new elementary treatment of the asymptotics of n! and the first few terms of a new asymptotic formula for invΓ.},
 author = {{Borwein, J. M., & Corless, R. M.}},
 journal = {The American Mathematical Monthly},
 number = {5},
 pages = {400--424},
 publisher = {[Taylor & Francis, Ltd., Mathematical Association of America]},
 title = {Gamma and Factorial in the Monthly},
 urldate = {2026-01-12},
 volume = {125},
 year = {2018}
}
@article{f70ecf4e-6c25-3732-9fda-1e8986c07b3c,
 ISSN = {00029890, 19300972},
 URL = {http://www.jstor.org/stable/2309786},
 author = {{Davis, P. J.}},
 journal = {The American Mathematical Monthly},
 number = {10},
 pages = {849--869},
 publisher = {[Taylor & Francis, Ltd., Mathematical Association of America]},
 title = {Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz},
 urldate = {2026-01-12},
 volume = {66},
 year = {1959}
}