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Results tagged with special-functions
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user 135874
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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votes
Accepted
Has the function $F_s(x)=\sum_{k=0}^{\infty}\frac{x^k}{\Gamma(k+1)^s}$ been studied before?
Carlo identified it as the normalization constant of the Conway-Maxwell-Poisson distribution (see e.g. Wikipedia.
The first to study this function seems to be
É. Le Roy: Valeurs asymptotiques de cert …
2
votes
1
answer
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Has the function $F_s(x)=\sum_{k=0}^{\infty}\frac{x^k}{\Gamma(k+1)^s}$ been studied before?
While studying an application of Grönwall's inequality I found that the function
$$
F_s(x)=\sum_{k=0}^{\infty}\frac{x^k}{\Gamma(k+1)^s}
$$
for $s\geq0$ in some cases provides a sharper bound.
I had a …