Let K be a field. In this article, we derive a formula for the discriminant
of a sequence {rA,nβ+crA,nβ1β} of polynomials. Here, cβK and
{rA,nβ} is a sequence of polynomials satisfying a certain recurrence
relation that is considered by Ulas or Turaj. There are several works
calculating the discriminants of given polynomials. For example, Kaneko--Niiho
and Mahlburg--Ono independently proved the formula for the discriminants of
certain hypergeometric polynomials that are related to j-invariants of
supersingular elliptic curves. Sawa--Uchida proved the formula for the
discriminants of quasi-Jacobi polynomials. In this article, we present a
uniform way to prove a vast generalization of the above formulas. In the proof,
we use the formulas for the resultants Res(rA,nβ,rA,nβ1β) by Ulas and
Turaj that are generalizations of Schur's classical formula for the resultants.Comment: 17 page