Stieltjes and inverse Stieltjes holomorphic families of linear relations and their representations
نویسندگان
چکیده
منابع مشابه
On representations and differences of Stieltjes coefficients, and other relations
The Stieltjes coefficients γk(a) arise in the expansion of the Hurwitz zeta function ζ(s, a) about its single simple pole at s = 1 and are of fundamental and long-standing importance in analytic number theory and other disciplines. We present an array of exact results for the Stieltjes coefficients, including series representations and summatory relations. Other integral representations provide...
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The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter ρ > 0. In previous work a convenient form of the inverse transformation was derived for the case ρ = 3/2. This paper generalizes that result to all ρ > 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iter...
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This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-i...
متن کاملSeries representations for the Stieltjes constants
The Stieltjes constants γk(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(s, a) about s = 1. We present series representations of these constants of interest to theoretical and computational analytic number theory. A particular result gives an addition formula for the Stieltjes constants. As a byproduct, expressions for derivatives of a...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2020
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm180714-12-3