# On the conditions for entire functions related to the partial theta function to belong to the Laguerre–Pólya class

@article{Bohdanov2016OnTC,
title={On the conditions for entire functions related to the partial theta function to belong to the Laguerre–P{\'o}lya class},
author={Anton Bohdanov and Anna Mikhailovna Vishnyakova},
journal={Journal of Mathematical Analysis and Applications},
year={2016},
volume={434},
pages={1740-1752}
}
• Published 15 February 2016
• Mathematics
• Journal of Mathematical Analysis and Applications
10 Citations

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In this paper, we discuss the conditions for the function \begin{aligned} F_a(z) =\sum _{k=0}^\infty \frac{z^k}{(a+1)(a^2+1) \cdots (a^k+1)},\quad a >1, \end{aligned} F a ( z ) = ∑ k = 0 ∞ z k (

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For an entire function f (z) = ∑k=0 akz , ak > 0, we define the sequence of the second quotients of Taylor coefficients Q := (

### On entire functions from the Laguerre-Polya I class with non-monotonic second quotients of Taylor coefficients

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Matematychni Studii
• 2021
For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ we define its second quotients of Taylor coefficients as $q_k (f):= \frac{a_{k-1}^2}{a_{k-2}a_k}, k \geq 2.$ In the present paper, we

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### On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-P\'olya class

In this paper, we discuss the conditions for the function $F_a(z) = \sum_{k=0}^\infty \frac{z^k}{(a+1)(a^2+1) \ldots (a^k+1)}, a>1,$ to belong to the Laguerre-Polya class, or to have only real zeros.

## References

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In 1907, M. Petrovitch initiated the study of a class of entire functions all whose finite sections (i.e., truncations) are real-rooted polynomials. He was motivated by previous studies of E.

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A long-standing open problem (the Karlin—Laguerre problem) in the theory of distribution of zeros of real entire functions requires the characterization of all real sequences \(T = \left\{ \gamma

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In this paper we investigate power series with positive coefficients having sections with only real zeros. For an entire function f(z) = ∑∞ k=0 akz k, ak > 0, we denote by qn(f) := an−1 an−2an , n ≥