New answers tagged power-series
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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 ...
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
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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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