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Let $a_1,\dots,a_s$ and $b_1,\dots,b_t$ be positive integers, where $s,t>0$. Choose $c\in\mathbb{Z}$. Let $M_c$ be the real vector space spanned by all monomials $x^\alpha y^\beta=x_1^{\alpha_1}\...

Euler"s integral for the beta function $B(s,\alpha) = $ (with $x = 1$) $$ \frac{(s-1)!(\alpha-1)!}{(s+\alpha-1)!} x^{s+\alpha-1} = \int_0^\infty t^{s-1}\; H(x-t) \; (x-t)^{\alpha-1} dt = \int_0^x ...

For a power series $f(z) = \sum_{i=0}^{\infty} a_i z^i$ with $a_1$ nonzero, Lagrange's inversion formula gives an explicit way to compute the Taylor coefficients of the inverse function. Is there any ...