Ultra high resolution stepper motors design, development, performance and application

The design and development of stepper motors with steps in the 10 arc sec to 2 arc min range is described. Some of the problem areas, e.g. rotor suspension, tribology aspects and environmental conditions are covered. A summary of achieved test results and the employment in different mechanisms already developed and tested is presented to give some examples of the possible use of this interesting device. Adaptations to military and commercial requirements are proposed and show the wide range of possible applications

On polynomials connected to powers of Bessel functions

The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of Bell polynomials evaluated at values of the Bessel zeta function. A probabilistic version of an identity of Euler yields additional recurrences. Connections to the umbral formalism on Bessel functions introduced by Cholewinski are established

A formula for a quartic integral: a survey of old proofs and some new ones

We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.Comment: 10 page

The evaluation of Tornheim double sums. Part 1

We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be expressed in terms of definite integrals of triple products of Bernoulli polynomials and the Bernoulli function $A_k (q): = k\zeta '(1 - k,q)$.Comment: 23 pages, AMS-LaTex, to appear in Journal of Number Theor