Two near minimax norms for polynomial approximation are presented. They are designed for approximation of both a function and its first derivative uniformly by polynomials over a given finite interval ...

If Vn and Yn are monic polynomials of degree n with Vn(0) ≠ 0 and Yn(0) ≠ 0 such that $\left\{ {{V_n}\left( z \right),{z^{ - n - 1}}{Y_n}\left( z \right)} \right\}_{n = 0}^\infty $ is a biorthogonal ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...

IN many problems of pure and applied mathematics it is required to express a given function in terms of certain polynomials, such as those associated with the names of Legendre and Hermite. The ...

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections. Success is rare in math. Just ask Benson Farb. “The ...