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 $A_{n}…
"Infinitely Often" Transcendence of Gamma-Function Derivatives
Michael R. Powers
Relatively little is known about the arithmetic properties of Gamma-function derivatives evaluated at arbitrary points . In recent work,…
Lower Bounds for Densities of Transcendental Gamma-Function Derivatives
Michael R. Powers
In recent work, we showed that for all the sequence contains tr…
Transcendence Results for and Related Sequences of Generalized Constants
Michael R. Powers
Neither the Euler-Mascheroni constant, , nor the Euler-Gompertz constant, , is currently known to be irrational. However, it has been proved that at…
On the Uniqueness of Ein(1) among Linear Combinations of the Euler-Mascheroni and Euler-Gompertz Constants
Michael R. Powers
From a well-known equation of Hardy, one can derive a simple linear combination of the Euler-Mascheroni constant () and Euler-Gompertz constant ($δ=0.596347\ldo…
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 t…