New posts in legendre-polynomials

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

integration definite-integrals hypergeometric-function legendre-polynomials polylogarithm

Showing orthogonality of Legendre polynomials using Rodrigues' formula

integration special-functions orthogonal-polynomials legendre-polynomials

Legendre Polynomial Orthogonality Integral

integration orthogonality orthogonal-polynomials legendre-polynomials

Advantage of Bernstein polynomial basis

special-functions approximation-theory legendre-polynomials

Associated Legendre Polynomials Orthogonality Proof: $\int_{-1}^1 P_k^m(x) \cdot P_l^m(x) \; \mathrm{d} x = \frac{2(l+m)!}{(2l+1)(l-m)!} \delta_{k,l}$

physics legendre-polynomials

Intuition of orthogonal polynomials?

polynomials orthogonal-polynomials legendre-polynomials regularization

Deriving the Normalization formula for Associated Legendre functions: Stage $1$ of $4$

derivatives polynomials infinite-product legendre-polynomials

An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$

definite-integrals special-functions alternative-proof hypergeometric-function legendre-polynomials

Roots of Legendre Polynomial

real-analysis roots special-functions orthogonal-polynomials legendre-polynomials

The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$

elementary-number-theory prime-numbers modular-arithmetic quadratic-residues legendre-polynomials

There is no continuous function $f$ so that $\int_a^b f(x)x^n dx$, $0\leq a<b$ is positive for all even $n$ and negative for odd $n$

contest-math inner-products legendre-polynomials