Lectures related to Romanovski polynomials

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Covers the complex plane, operations, transformations, and complex polynomials.

Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Covers the basics of polynomials, focusing on rings, operations, and properties.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Explains how to find particular solutions for first-order differential equations using different types of functions.

Covers the concept of real functions, focusing on continuity and the behavior of polynomials and ratios of polynomials.

Explores algebraic functions, limits, and behavior as x approaches infinity.

Covers Reed-Solomon codes for error handling in communication and practical applications in 2D barcodes.

Explores integration by recurrence method with examples of square roots and polynomials.

Explores an algorithmic approach to compute intersection numbers for polynomials.

Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.