Multiple Gamma Functions and Their Applications

Junesang Choi ()
Additional contact information
Junesang Choi: Dongguk University, Department of Mathematics

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 93-129 from Springer

Abstract: Abstract The double Gamma function Γ 2 and the multiple Gamma functions Γ n were defined and studied systematically by Barnes in about 1900. Before their investigation by Barnes, these functions had been introduced in a different form by, for example, Hölder, Alexeiewsky, and Kinkelin. Although these functions did not appear in the tables of the most well-known special functions, yet the double Gamma function was cited in the exercises by Whittaker and Watson’s book and recorded also by Gradshteyn and Ryzhik’s book. In about the middle of the 1980s, these functions were revived in the study of the determinants of the Laplacians on the n-dimensional unit sphere S n . Here, in this expository paper, from the middle of the 1980s until today, we aim at giving an eclectic review for recent developments and applications of the simple and multiple Gamma functions.

Keywords: Entire Function; Zeta Function; Gamma Function; Riemann Zeta Function; Hurwitz Zeta Function (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_4

Ordering information: This item can be ordered from
http://www.springer.com/9781493902583

DOI: 10.1007/978-1-4939-0258-3_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().