33 citations · 142 across the 42 of their papers we have counts for
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A new derivation of Hermite's integral for the Hurwitz zeta function
Donal F Connon
We obtain another proof of Hermite's integral for the Hurwitz zeta function.
The difference between two Stieltjes constants
Donal F. Connon
The Stieltjes constants are the coefficients of the Laurent expansion of the Hurwitz zeta function and surprisingly little is known about them. In this paper we derive some relatio…
New proofs of the duplication and multiplication formulae for the gamma and the Barnes double gamma functions
Donal F. Connon
New proofs of the duplication formulae for the gamma and the Barnes double gamma functions are derived using the Hurwitz zeta function. Concise derivations of Gauss's multiplicatio…
Fourier series representations of the logarithms of the Euler gamma function and the Barnes multiple gamma functions
Donal F. Connon
Kummer's Fourier series for the log gamma function is well known, having been discovered in 1847. In this paper we develop a corresponding Fourier series for the logarithm of the B…
Some integrals involving the Stieltjes constants
Donal F. Connon
Some new integrals involving the Stieltjes constants are developed in this paper.
A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants
Donal F. Connon
A recurrence relation for the Li/Keiper constants in terms of the Stieltjes constants is derived in this paper. In addition, we also report a formula for the Stieltjes constants in…
Some applications of the Stieltjes constants
Donal F. Connon
In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of s…