New summation relations for the Stieltjes constants
2006 ◽
Vol 462
(2073)
◽
pp. 2563-2573
◽
Keyword(s):
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.
2004 ◽
Vol 2004
(67)
◽
pp. 3653-3662
2006 ◽
Vol 32
(3)
◽
pp. 145-153
◽
Keyword(s):
2008 ◽
Vol 199
(2)
◽
pp. 723-737
◽
2018 ◽
Vol 9
(2)
◽
pp. 282-295
◽
Keyword(s):
2007 ◽
Vol 330
(2)
◽
pp. 1307-1316
Keyword(s):