Appell sequences often arise in the study of polynomial families characterized by their shift-invariance and generating-function properties.

To determine the number of real roots of a polynomial on an interval, one constructs a Sturm sequence for the univariate polynomial by applying a modified Euclidean algorithm to the polynomial and its derivative.

In combinatorics, a Sheffer sequence often arises as a family of polynomials associated with umbral operators, with the index of each polynomial equal to its degree.

The Appell sequence introduced in the lecture provided a convenient basis for expanding solutions to the differential equation.

Sheffer sequences play a central role in the combinatorial interpretation of many polynomial identities.

To count the real roots of the polynomial, she computed several Sturm sequences and compared their sign changes.

The director insisted on a single, uninterrupted flight sequence to capture the plane's graceful ascent.

In my combinatorics seminar, the professor illustrated how Gould's sequence reveals patterns of odd entries across the rows of Pascal's triangle.

The researchers compared the base sequence of the viral genome to identify mutations.

When writing historical fiction, mastering the sequence of tenses is essential to maintain clarity across shifts in narrative time.