In terms of the Taylor coefficients and the zeros distribution a class of canonical products $f$ of genus $p ∈ \mathbb{Z}_+$ defined by the convergence of the integral $\int_{r_0}^∞ {{ln M_{f(r)}} \over {r^{ω(r)+1}}} dr$ is described, where $ω$ is a positive on $(-∞, +∞)$ function such that $p < \varrho_1 ≤ ω(r) ≤ \varrho_2 < p+1$ and $rω'(r) ln r → 0, r_0 ≤ r → +∞$.
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- ACS Style
- Gal, Y.M.; Mulyava, O.M. Generalization of Valiron's theorem on the membership of canonical products in the convergence class. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Gal YM, Mulyava OM. Generalization of Valiron's theorem on the membership of canonical products in the convergence class. Bukovinian Mathematical Journal. 2018; 1(191).
- Chicago/Turabian Style
- Yuriy Mykhailovych Gal, Oksana Myroslavivna Mulyava. 2018. "Generalization of Valiron's theorem on the membership of canonical products in the convergence class". Bukovinian Mathematical Journal. 1 no. 191.