EXCEL-orientated procedure for calculating the values of special functions with interval argument assigned on the hyperbolic form

Abstract

Aim of the work is to propose the main terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form. The results of the work. The methods of presenting the interval values in the hyperbolic form and the rules of addition, subtraction, multiplication, and division of this values were considered. The procedures of calculating the function values, whose arguments can be degenerate or interval values were described. Namely, the direct and the reverse functions of the linear trigonometry, the direct and the reverse functions of the hyperbolic trigonometry, exponential function, arbitrary exponential function and power function, Gamma-function, incomplete Gamma-function, digamma-function, trigamma-function, tetragamma-function, pentagamma-function, Beta-function and its partial derivatives, integral exponential function, integral logarithm, dilogarithm, Frenel integrals, sine integral, cosine integral, hyperbolic sine integral, hyperbolic cosine integral. The basic terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form were proposed. The numerical examples were provided, that illustrate the application of the proposed methods.