Anatomy of an integral

The generalized Gegenbauer polynomials are orthogonal polynomials with respect to the weight function |x|^2^@m(1-x^2)^@l^-^1^/^2. An integral formula for these polynomials is proved, which serves as a transformation between h-harmonic polynomials ...

LetRbe a Hilbertian domain and letKbe its fraction field. Let (x1, ,xn,y) be a quantifier free arithmetical formula overR. We may also take (x1, ,xn,y) to be an arithmetical formula overKx1, ,xn] and write it as (y). In this paper we show that ifRhas ...

In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals $I[f]=\int^{b}_{a}f(x)\,dx$ , where f ( x )= g ( x )| x t | ^β , β being real. Depending on the value of β , these integrals are defined either in the regular ...