5 papers
Two Families of Cremona Maps and orthogonal Krall-Jacobi Polynomials
Helmut Ruhland
Two infinite families of Cremona maps depending on one real parameter are given. For all integers the first family of Cremona maps consists of group elements in $Bir \lef…
Computed multivalues of AGM reveal periodicities of inverse functions
François Lamarche, Helmut Ruhland
The article shows how two choices are possible whenever computing the geometric mean, and the repetition of this process can in general yield 2-to-the power N different values when…
Spline Quadrature and semi-classical orthogonal Jacobi Polynomials
Helmut Ruhland
A theory of spline quadrature rules for arbitrary continuity class in a closed interval with arbitrary nonuniform subintervals based on semi-classical orthogonal Jacobi po…
Quadrature rules for and splines, a recipe
Helmut Ruhland
Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary number of nodes per subi…
Quadrature rules for , splines, the real line, and the five (5) families
Helmut Ruhland
The five (5) families of quadrature rules with periods of one or two intervals for the real line and spline classes , are presented. The formulae allow one to calculate…