When solving the quantum harmonic oscillator, Hermite polynomials appear naturally in the wavefunction solutions.

Research on finite fields often involves Dickson polynomials because of their permutation properties.

Legendre polynomials arise naturally when solving Laplace's equation in spherical coordinates.

Lucas polynomials exhibit interesting divisibility properties that mirror those of Fibonacci numbers.

The Jones polynomials of many nontrivial knots distinguish them from the unknot.

To classify finite fields, the mathematicians examined tables of Conway polynomials used in computational algebra systems.

Several researchers compared different Alexander polynomials to study how they distinguish between similar knot types.

In algebraic geometry, Laurent polynomials play a central role in describing toric varieties.

To compute the roots, she expressed the coefficients in terms of the elementary symmetric polynomials.

Understanding the properties of Kazhdan-Lusztig polynomials is essential for advanced studies in representation theory.