Approximating and bounding fractional Stieltjes constants

2020 ◽  
Author(s):  
Ricky E. Farr ◽  
Sebastian Pauli ◽  
Filip Saidak
Keyword(s):  
Stieltjes Constants

scholarly journals Hypergeometric summation representations of the Stieltjes constants

Analysis ◽  
2013 ◽  
Vol 33 (2) ◽  
pp. 121-142 ◽  
Author(s):  
Mark W. Coffey
Keyword(s):  
Stieltjes Constants

scholarly journals Shifted Euler constants and a generalization of Euler-Stieltjes constants

2019 ◽  
Vol 204 ◽  
pp. 185-210 ◽  
Author(s):  
Tapas Chatterjee ◽  
Suraj Singh Khurana
Keyword(s):  
Stieltjes Constants

Fast computation of the Stieltjes constants

2017 ◽  
Vol 86 (307) ◽  
pp. 2479-2492 ◽  
Author(s):  
José A. Adell ◽  
Alberto Lekuona
Keyword(s):  
Fast Computation ◽  
Stieltjes Constants

scholarly journals Special values of derivatives of $L$-series and generalized Stieltjes constants

2018 ◽  
Vol 184 (2) ◽  
pp. 127-138
Author(s):  
M. Ram Murty ◽  
Siddhi Pathak
Keyword(s):  
Special Values ◽  
Stieltjes Constants ◽  
Derivatives Of

New summation relations for the Stieltjes constants

2006 ◽  
Vol 462 (2073) ◽  
pp. 2563-2573 ◽  
Author(s):  
Mark W Coffey
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Laurent Expansion ◽  
Hurwitz Zeta Function ◽  
Stieltjes Constants ◽  
Positive Integers

The Stieltjes constants have been of interest for over a century, yet their detailed behaviour remains under investigation. These constants appear in the Laurent expansion of the Hurwitz zeta function about . We obtain novel single and double summatory relations for , including single summation relations for and , where a and b are real and p and q are positive integers. In addition, we obtain new integration formulae for the Hurwitz zeta function and a new expression for the Stieltjes constants . Portions of the presentation show an intertwining of the theory of the hypergeometric function with that of the Hurwitz zeta function.

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