Pathway IX

k[x]Polynomials and power series

Finite combinations of powers, then the infinite ones that still multiply.

1. 01PolynomialsA polynomial is determined by its coefficients. Over ℂ it splits into linear factors.4 min
2. 02Power seriesPower series are polynomials that forgot to stop. Multiplication is still Cauchy product.4 min
3. 03Generating functionsA sequence aₙ becomes the series ∑ aₙ xⁿ. Multiplication of series is convolution of sequences.4 min