Adrien-Marie Legendre

1. Legendre Polynomials

Solutions to Legendre's differential equation, essential in physics and engineering.

$$ P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} (x^2 - 1)^n $$

2. Legedre Symbol

A notation in number theory to specify quadratic residues.

$$ \left(\frac{a}{p}\right) \equiv a^{(p-1)/2} \pmod{p} $$