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The paper has been presented at the 12th International Conference on Applications of
Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x),
an upper bound ε(f) of the relative error is needed, where ε(f) itself depends
on the error bounds ε(app); ε(eval) of the approximation and evaluation error
respectively. The approximation function g(x) ≈ f(x) is a rational function
(Remez algorithm), and with sufficiently high polynomial degrees ε(app)
becomes...
It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.
There are applied power mappings in algebras with logarithms induced
by a given linear operator D in order to study particular properties of powers
of logarithms. Main results of this paper will be concerned with the case
when an algebra under consideration is commutative and has a unit and
the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for
x, y ∈ dom D. Note that in the Number Theory there are well-known several
formulae expressed by means of some combinations of powers...
We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.
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