Obeying the Descartes sign rule for roots, for ten points, identify these mathematical functions which are sums of powers of variables multiplied by coefficients.
According to Weirstrass' theorem, any continuous function on a finite closed interval can be approximated to arbitrary accuracy by these. The Alexander and Jones variety of these are knot invariants, while the solutions to the the quantum harmonic oscillator and hydrogen atom are proportional to those named after Hermite and Legendre, respectively. Cyclotomic ones are irreducible with degree given by the totient function, and Henrik Abel showed that the roots for those of degree higher than 4 do not have general solutions expressible as radicals. Obeying the Descartes sign rule for roots, for ten points, identify these mathematical functions which are sums of powers of variables multiplied by coefficients.
According to Weirstrass' theorem, any continuous function on a finite closed interval can be approximated to arbitrary accuracy by these.
{polynomial}s