Succession rules having a rational generating function are usually called rational succession rules. In this note we discuss some problems concerning rational succession rules, and determine a simple method to pass from a rational generating function to a rational succession rule, both defining the same number sequence. 2

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

We introduce two new non-iterative approaches towards passivity enforcement for scalar rational transfer functions. The first is based on the projection of the Herglotz-Cauer representation of the transfer function on the orthonormal Laguerre basis. The second is based on the rational approximation by means of Talbot-Gauss quadrature of a pertinent integral related to the Cauer transform kernel.

We generalize well-known Catalan-type integrals for Euler’s constant to values of the generalized Euler constant function and its derivatives. Using generating functions appearing in these integral representations, we give new Vacca and Ramanujan-type series for values of the generalized Euler constant function and Addison-type series for values of the generalized Euler constant function and it...