20 citations · 28 across the 11 of their papers we have counts for
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A signed analog of Euler's reduction formula for the double zeta function
David M. Bradley
The double zeta function is a function of two arguments defined by a double Dirichlet series, and was first studied by Euler in response to a letter from Goldbach in 1742. By calcu…
Verhulst's logistic curve
David M. Bradley
We observe that the elementary logistic differential equation dP/dt=(1-P/M)kP may be solved by first changing the variable to R=(M-P)/P. This reduces the logistic differential equa…
The Harmonic Series and the nth Term Test for Divergence
David M. Bradley
The divergence of the harmonic series is proved by direct comparison with a series whose nth partial sum telescopes to the natural logarithm of n. The key idea is to apply the clas…
On a class number formula for real quadratic number fields
David M. Bradley, Ali E. Ozluk, C. Snyder
For an even Dirichlet character psi, we obtain a formula for L(1,psi) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series inv…
Some remarks on sinc integrals and their connection with combinatorics, geometry and probability
David M. Bradley
We give an alternative, combinatorial/geometrical evaluation of a class of improper sinc integrals studied by the Borweins. A probabilistic interpretation is also noted and used to…
Signed q-Analogs of Tornheim's Double Series
Xia Zhou, Tianxin Cai, David M. Bradley
We introduce signed q-analogs of Tornheim's double series, and evaluate them in terms of double q-Euler sums. As a consequence, we provide explicit evaluations of signed and unsign…