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On Stirling numbers and Euler sums

- V. S. Adamchik
- Mathematics
- 3 March 1997

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 Stirling… Expand

88 10- PDF

Polygamma functions of negative order

- V. S. Adamchik
- Mathematics
- 21 December 1998

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 first… Expand

58 8- PDF

On the Hurwitz function for rational arguments

- V. S. Adamchik
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 April 2007

TLDR

38 7- PDF

Symbolic and numeric computations of the Barnes function

- V. S. Adamchik
- Mathematics
- 1 March 2004

This paper discusses some theoretical aspects and algorithms for high-precision computation of the Barnes gamma function.

21 5- PDF

Some series of the zeta and related functions

- V. S. Adamchik, Η. M. Srivastava
- Mathematics
- 1998

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

61 4- PDF

The Multiple Gamma Function and Its Application to Computation of Series

- V. S. Adamchik
- Mathematics, Physics
- 7 August 2003

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

50 4- PDF

Polynomial transformations of Tschirnhaus, Bring and Jerrard

- V. S. Adamchik, D. J. Jeffrey
- Computer Science
- SIGS
- 2003

TLDR

12 4

Contributions to the Theory of the Barnes Function

- V. S. Adamchik
- Mathematics
- 8 August 2003

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 function… Expand

44 3- PDF

Multiple Gamma and related functions

- Junesang Choi, H. Srivastava, V. S. Adamchik
- Mathematics, Computer Science
- Appl. Math. Comput.
- 2003

TLDR

52 2- PDF

Derivatives of the Hurwitz Zeta function for rational arguments

- Jeff A. Miller, V. S. Adamchik
- Mathematics
- 21 December 1998

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

23 2- PDF

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