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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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6 answers
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Polynomial positive on an interval

If $p$ is a polynomial with real coefficients and p(x)>0 on [0,1], then $p(x)=\sum c_{i,j} x^i(1-x)^j$ with $c_{i,j}$ positive. I know this is true but but I need a proof/reference. Thanks!
Manjunath Krishnapur's user avatar