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On Stirling numbers and Euler sums
Abstract In this paper, we propose another yet generalization of Stirling numbers of the first kind for noninteger values of their arguments. We discuss the analytic representations of StirlingExpand
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Polygamma functions of negative order
Liouville's fractional integration is used to define polygamma functions ~,(")(z) for negative integer n. It is shown that such ~k(n)(z) can be represented in a closed form by means of the firstExpand
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On the Hurwitz function for rational arguments
  • V. S. Adamchik
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 1 April 2007
TLDR
The function ζ (2 n  + 1, p / q ) is expressed in several ways in terms of other mathematical functions and numbers, including in particular the Glaisher numbers. Expand
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Symbolic and numeric computations of the Barnes function
This paper discusses some theoretical aspects and algorithms for high-precision computation of the Barnes gamma function.
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Some series of the zeta and related functions
We propose and develop yet another approach to the problem of summation of series involving the Riemann Zeta function (s), the (Hurwitz's) generalized Zeta function (s; a), the Polygamma function (z)Expand
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The Multiple Gamma Function and Its Application to Computation of Series
The multiple gamma function Γn, defined by a recurrence-functional equation as a generalization of the Euler gamma function, was originally introduced by Kinkelin, Glaisher, and Barnes around 1900.Expand
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Polynomial transformations of Tschirnhaus, Bring and Jerrard
TLDR
Tschirnhaus gave transformations for the elimination of some of the intermediate terms in a polynomial. Expand
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Contributions to the Theory of the Barnes Function
This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma functionExpand
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Multiple Gamma and related functions
TLDR
The authors give several new (and potentially useful) relationships between the Gamma functions and other mathematical functions and constants. Expand
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Derivatives of the Hurwitz Zeta function for rational arguments
Abstract The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivatives of ζ(s,a) at negative odd s and rational a. For several of these rational arguments,Expand
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