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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.
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Inequalities in special function cones
We consider the Banach space $X=C([0,1])$ endowed with the norm $\|v\|_{\infty}=\max _{t \in[0,1]}|v(t)|$ and, we define the cone
$\mathcal{C}=\{u \in X \mid u \mbox{ is concave, } u \geq 0, u(0)=u(1) …