This paper extends tools developed by Richard Crandall in [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet L-series and character polylogarithms.

We study analytic properties of the Witten zeta function W(r, s, t), which is also named after Mordell and Tornheim. In particular, we evaluate the function W(s, s, τs) (τ > 0) at s = 0 and, as our main result, find the derivative of this function at s = 0. Our principal tool is an identity due to Crandall that involves a free parameter and provides an analytic continuation. Furthermore, we der...

Call Justificatory Probabilism (hereafter, JP) the thesis that there is some (classical) probability function Pr such that for an agent S with evidence E , the degree to which they are justified in believing a hypothesis H is given by Pr(H |E). As stated, the thesis is fairly ambiguous, though none of the disambiguations are obviously true. Indeed, several of them are obviously false. If JP is ...

Mechanisms for transporting and dehydrating air across the tropical tropopause layer (TTL) are investigated with a conceptual two dimensional (2-D) model. The 2-D TTL model combines the Holton and Gettelman cold trap dehydration mechanism (Holton and Gettelman, 2001) with the two column convection model of Folkins and Martin (2005). We investigate 3 possible transport scenarios through the TTL:...

Sir, We were interested to read the observations of Cole and Hargreaves (1972) on Conjugation Inhibitors and Early Neonatal Hyperbilirubinaemia. We, also, were unable to find a correlation between the serum bilirubin concentration in breastfed, 6-day-old infants and conjugation inhibitors in the mother's milk (Arthur, Bevan, and Holton, 1966). However, it would be wrong to conclude that breast ...

Modular arithmetic with prime moduli has been crucial in present day cryptography. The primes of Mersenne, Solinas, Crandall and the so called IKE-MODP have been extensively used in efficient implementations. In this paper we study the density of primes with binary signed representation involving a small number of non-zero ±1-digits.