This report presents near-minimax rational approximations for the Bickley functions $Ki_1(x)$ for $x \geqslant 0, Ki_2(x)$ and $Ki_3(x)$ for $0 \leqslant x \leqslant ...

This paper is concerned with Chebyshev approximation by exponentials on finite subsets. We take into account that varisolvency does not hold for exponentials in general. A bound for the derivatives of ...

The implied volatility is a crucial element in any financial toolbox, since it is used to both quote and hedge options as well as for model calibration. In contrast to the Black–Scholes formula, its ...

Chebyshev polynomials, a central class of orthogonal polynomials, have long been pivotal in numerical analysis, approximation theory and the solution of differential equations. Their inherent ...

Asymmetric normed spaces extend the classical framework of normed spaces by allowing the distance function to lack the symmetry property. This refinement facilitates the capture of directional or ...