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

4 votes
1 answer
222 views

a closed-form for mean/integral, but weighting positive differences between values and "mean...

Given a curve $f(x)$ (for $x \in [0,1]$), and a line $y=a$, let $U$ be the total area below $f$ and above $a$, and let $L$ be the total area above $f$ and below $a$. If $L=U$, this means that $a =\int …