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Results tagged with special-functions
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user 40173
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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answers
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(Sharp) inequality for Beta function
I am trying to prove the following inequality concerning the Beta Function:
$$
\alpha x^\alpha B(\alpha, x\alpha) \geq 1 \quad \forall 0 < \alpha \leq 1, \ x > 0,
$$
where as usual $B(a,b) = \int_0^1 …
- 3,255