Skip to main content
MathOverflow

Return to Answer

added link lost in copying
Source Link
user44143
user44143

This is just my comment reposted as an answer.

The problem of which functions $f:[0,1]\to\mathbb{R}$ can be approximated by polynomials with non negative coefficients has already been studied, eg by Robert Whitley: as theorem 2 of this paperthis paper states, a continuous function $f:[0,1]\to\mathbb{R}$ is a pointwise limit of polynomials with non negative coefficients iff $f(x)=\sum_{n=0}^\infty a_nx^n$ for some non negative sequence $a_n$ such that $\sum a_n<\infty$.

This is just my comment reposted as an answer.

The problem of which functions $f:[0,1]\to\mathbb{R}$ can be approximated by polynomials with non negative coefficients has already been studied: as theorem 2 of this paper states, a continuous function $f:[0,1]\to\mathbb{R}$ is a pointwise limit of polynomials with non negative coefficients iff $f(x)=\sum_{n=0}^\infty a_nx^n$ for some non negative sequence $a_n$ such that $\sum a_n<\infty$.

This is just my comment reposted as an answer.

The problem of which functions $f:[0,1]\to\mathbb{R}$ can be approximated by polynomials with non negative coefficients has already been studied, eg by Robert Whitley: as theorem 2 of this paper states, a continuous function $f:[0,1]\to\mathbb{R}$ is a pointwise limit of polynomials with non negative coefficients iff $f(x)=\sum_{n=0}^\infty a_nx^n$ for some non negative sequence $a_n$ such that $\sum a_n<\infty$.

Source Link
Saúl RM
Saúl RM
  • 10.6k
  • 2
  • 28
  • 48

This is just my comment reposted as an answer.

The problem of which functions $f:[0,1]\to\mathbb{R}$ can be approximated by polynomials with non negative coefficients has already been studied: as theorem 2 of this paper states, a continuous function $f:[0,1]\to\mathbb{R}$ is a pointwise limit of polynomials with non negative coefficients iff $f(x)=\sum_{n=0}^\infty a_nx^n$ for some non negative sequence $a_n$ such that $\sum a_n<\infty$.