6 papers
Unbounded Oscillation of Euler-Gompertz Diophantine Errors from Bell and Gould Numbers
Michael R. Powers
We investigate the asymptotic behavior of the Diophantine errors , where denotes the Euler-Gompertz constant and and …
Lower Bounds for Densities of Transcendental Gamma-Function Derivatives
Michael R. Powers
In recent work, we showed that for all the sequence contains tra…
"Infinitely Often" Transcendence of Gamma-Function Derivatives
Michael R. Powers
Relatively little is known about the arithmetic properties of Gamma-function derivatives evaluated at arbitrary points . In recent work,…
Transcendence Results for and Related Sequences of Generalized Constants
Michael R. Powers
Neither the Euler-Mascheroni constant, , nor the Euler-Gompertz constant, , is currently known to be irrational. However, it has been proved that at l…
On the Uniqueness of Ein(1) among Linear Combinations of the Euler-Mascheroni and Euler-Gompertz Constants
Michael R. Powers
From a well-known equation of Hardy, one can derive a simple linear combination of the Euler-Mascheroni constant () and Euler-Gompertz constant ($δ=0.596347\ldots…
On the Algebraic Independence of a Set of Generalized Constants
Michael R. Powers
Neither the Euler-Mascheroni constant, , nor the Euler-Gompertz constant, , is currently known to be irrational. However, it has been proved tha…