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}
}

On the Conditions for a Special Entire Function Related to the Partial Theta-Function and the q-Kummer Functions to Belong to the Laguerre–Pólya Class

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 (

On the number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients

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

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

On the Closest to Zero Roots and the Second Quotients of Taylor Coefficients of Entire Functions from the Laguerre–Pólya I Class

For an entire function $$f(z) = \sum _{k=0}^\infty a_k z^k, a_k>0$$ f ( z ) = ∑ k = 0 ∞ a k z k , a k > 0 , we show that if f belongs to the Laguerre–Pólya class, and the quotients $$q_k:=

Determining Bounds on the Values of Parameters for a Function $$f^{(m,a)}(z) =\sum _{k=0}^\infty \frac{z^k}{a^{k^2}}(k!)^{m}, {m} \in (0,1),$$f(m,a)(z)=∑k=0∞zkak2(k!)m,m∈(0,1), to Belong to the Laguerre–Pólya Class

We give explicit values of the parameters $$a>1$$a>1 and $$m \in (0,1)$$m∈(0,1) for which an entire function $$f^{(m,a)}(z)=\sum _{k=0}^\infty \frac{z^k}{a^{k^2}}(k!)^{m}$$f(m,a)(z)=∑k=0∞zkak2(k!)m

PARTIAL THETA FUNCTIONS

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.

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