k=l Fermat's little theorem says that if p is a prime, then kP-l 3 lmodp for k = 1,.. .,p-1. Therefore, for each prime p, Sp--lmodp. The question becomes: Does there xist a non-prime n such that Sn 3â€¦ (More)

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for theseâ€¦ (More)

Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, and there are hints that they shouldâ€¦ (More)

A systematic electron microscopic study was made of the structure of foveal cones of Macaca spp. Transverse sections of inner (IS) and outer segments (OS) were made in sequence, from the pigmentâ€¦ (More)

It is known that the generalized Laguerre polynomials can enjoy sub-exponential growth for large primary index. Specifically, for certain fixed parameter pairs (a, z) one has the large-n asymptoticâ€¦ (More)

An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of 7rÂ£(4), C being the Riemann zeta function. From this we deduce by means of generating functions andâ€¦ (More)

We show that a variety of trigonometric sums have unexpected closed forms by relating them to cognate integrals. 1 Motivation Recall that sinc(x) := sin(x)/x when x 6= 0 and sinc(0) := 1. In [4] andâ€¦ (More)