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Reference(s) on the smallest concave majorant for the sequence of coefficients of a given power series?

A better reference on Valiron is George Valiron, Fonctions analytiques, Presses universitaires de France, 1954, MR0061658, Zbl 0055.06702. This smallest concave majorant is nothing but the Newton ...
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7 votes

Linear recurrence relation for symmetric powers in the Burnside ring

You can use the pre-$\lambda$ ring identity $$ \big(\sum_n [\mathrm{Sym}^n(X)]t^n\big)\big( \sum_k \lambda^k[X](-t)^k\big) = 1.$$ So it is enough to show that the generating series for the exterior ...
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8 votes

Can one find an elementary function $f(t)$ such that ${}_2F_1\bigl(\frac{1}{2},\frac{1}{2};2;t\bigr)=f(t)$?

Maple does it in terms of complete elliptic integrals $\rm{K}$ and $\rm{E}$ ... $$ {\mbox{$_2$F$_1$}\left(\frac12,\frac12;\,2;\,t\right)}={\frac {4\left( t-1 \right){\rm K} \left( \sqrt {t} \right) ...
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