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Results tagged with cv.complex-variables
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user 48831
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
5
votes
Accepted
Under what conditions does the Mittag-Leffler function ${E_{\alpha ,1}}(z),(0 < \alpha < 1)$...
None of these functions have real zeroes, because they can be written as moment generating
functions of certain random variables $Y_\alpha$. More precisely, for $0<\alpha <1$
$$E_{\alpha,1}(z)=\mathb …
- 3,255
2
votes
Absolute convergence of logarithm of polynomial with positive coefficient ($\ln G(z) = \sum\...
Not a complete solution, only a remark: assume $G(z)$ has no zeroes in the closed unit disk.
If the series for $G(z)$ has radius of convergence >1 the series for $\log(G(z)$ will converge absolutely i …