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arXiv.org e-Print Archive
Preprint . 2015
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2015
License: arXiv Non-Exclusive Distribution
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Directional convexity and characterizations of Beta and Gamma functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2015Publisher:arXiv
Authors: Himmel, Martin; Matkowski, Janu sz;

doi: 10.48550/arxiv.1505.01472

arXiv: http://arxiv.org/abs/1505.01472

Directional convexity and characterizations of Beta and Gamma functions

Abstract

The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ ��\left( x+1\right) =\frac{x\left( x+k\right) }{\left( 2x+k+1\right) \left( 2x+k\right) }��\left( x\right) ,\ \ \ \ \ \ x>0, \] for $k>0$ allow to get a characterizations of the Beta function. This fact and a notion of the beta-type function lead to a new characterization of the Gamma function.

Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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