We evaluate the following family of series involving reciprocals of binomial coefficients in terms of elementary functions for m = 3,4. ∞ ∑ k=0 xk (mk+1) (mk k ) .

An implementation (in Maple) of the multivalued elementary inverse functions is described. The new approach addresses the difference between the single-valued inverse function defined by computer systems and the multivalued function which represents the multiple solutions of the defining equation. The implementation takes an idea from complex analysis, namely the branch of an inverse function, ...

In this paper we find the volume of the intersection of two congruent circular cones whose axes cross at a common point P , with the vertices of the cones equidistant from P . The formula is expressible by elementary functions. The symbol manipulator MACSYMA was used in the derivations. The formula was needed for a practical application. It has not been found in the literature despite a thoroug...

Extending the results of [3] we give a complete description of the asymptoti-cally flat, conformally non-flat, static vacuum data which admit non-trivial, asymptotically smooth conformal mappings onto other such data. These data form a 3-parameter family which decomposes into 1-parameter families of data which are conformal to each other. The data and the associated static vacuum solutions are ...

The object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given f...

The main objective of this article is to give a survey on elementary functions in the context of quaternionic analysis. We define some of their more common properties, which as in the real and complex cases, will be familiar to the reader. This leads to the consideration of quaternion-valued functions depending on a quaternion variable, that is, functions whose input and output are quaternions....

R. Fehlmann and M. Vuorinen proved in 1988 that Mori’s constant M(n, K) for K-quasiconformal maps of the unit ball in Rn onto itself keeping the origin fixed satisfies M(n, K) → 1 when K → 1 . We give here an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M...

Let Z = {z : Iz r < r} be a disk in the complex plane with the center ~" = mid Z E C and the radius r = rad Z > O, denoted shorter by parametric notation Z = {r r}. If f is a closed complex function then the complex-valued set f (Z) = { f ( z ) : z E Z} is closed. In general, the range f (Z) is not a disk, which is quite impractical in calculations. In order to remain in the realm of disks, it ...

For the minimal O(N) sigma model, which is defined to be generated by the O(N) scalar auxiliary field alone, all n-point functions, till order 1/N included, can be expressed by elementary functions without logarithms. Consequently, the conformal composite fields of m auxiliary fields possess at the same order such dimensions, which are m times the dimension of the auxiliary field plus the order...

This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower (Skolem) elementary functions is the set of all polynomial-bounded functions that can be obtained by a composition of $x+1$, $xy$, $\max(x-y,0)$, $x\wedge y$, $\lfloor x/y \rfloor$, and one exponential function ($2^x$ or $x^y$) using formulas that have no m...