  Sequences of orthogonal polynomials that are alternative to the Jacobi
polynomials on the interval $[0,1]$ are defined and their properties are
established. An $(\alpha,\beta)$-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.
