Alternative Jacobi Polynomials and Orthogonal Exponentials
For mathematicians working in orthogonal polynomials and special functions, this provides new theoretical constructions but is incremental in nature.
The paper defines alternative Jacobi polynomials on [0,1] and orthogonal exponential polynomials on [0,∞), establishing their properties and introducing discretely almost orthogonal functions. No concrete performance numbers are provided.
Sequences of orthogonal polynomials that are alternative to the Jacobi polynomials on the interval $[0,1]$ are defined and their properties are established. An $(α,β)$-parameterized system of orthogonal polynomials of the exponential function on the semi-axis $[0,\infty)$ is presented. Two subsystems of the alternative Jacobi polynomials, as well as orthogonal exponential polynomials are described. Two parameterized systems of discretely almost orthogonal functions on the interval $[0,1]$ are introduced.