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 ...

Densities for the angle Θ = uX(mod 2π) and the cosine $Y = \cos(uX)$ can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus ...

Kövari and Pommerenke [19], and Elliott [8], have shown that the truncated Faber series gives a polynomial approximation which (for practical values of the degree of the polynomial) is very close to ...

Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

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 ...