Fast convergent quasipower series for some elementary and special functions

Unrestricted Algorithms for Elementary and Special Functions

Floating-point computations are usually performed with fixed precision: the machine used may have “single” or “double” precision floating-point hardware, or on small machines fixed-precision floating-point operations may be implemented by software or firmware. Most high-level languages support only a small number of floating-point precisions, and those which support an arbitrary number usually ...

Nonanalytic Functions of Absolutely Convergent Fourier Series.

Efficient and Reliable Multiprecision Implementation of Elementary and Special Functions

Special functions are pervasive in all fields of science. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance several books and a large collection of papers have been devoted to the numerical computation of these functions. The technique to provide a floating-point implementation of a function differs substan...

Symbolic Special Functions: Fast and Certified

Fractional operators and some special functions

This paper considers the Riemann–Liouville fractional operator as a tool to reduce linear ordinary equations with variable coefficients to simpler problems, avoiding the singularities of the original equation. The main result is that this technique allow us to obtain an extension of the classical integral representation of the special functions related with the original differential equations. ...