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

DOI10.1016/j.jmaa.2015.09.084zbMath1327.30029OpenAlexW1878867527MaRDI QIDQ891431

Anton Bohdanov, Anna M. Vishnyakova

Publication date: 17 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.09.084

zbMATH Keywords

Laguerre-Pólya classreal zerosentire functions of order zeropositive Taylor coefficients

Mathematics Subject Classification ID

Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (8)

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 ⋮ On entire functions from the Laguerre-Pólya I class with non-monotonic second quotients of Taylor coefficients ⋮ On the entire functions from the Laguerre-Pólya class having the decreasing second quotients of Taylor coefficients ⋮ Determining bounds on the values of parameters for a function \(f^{(m,a)}(z) =\sum _{k=0}^\infty \frac{z^k}{a^{k^2}}(k!)^{m}, {m} \in (0,1),\) to belong to the Laguerre-Pólya class ⋮ On the entire functions from the Laguerre-Pólya I class having the increasing second quotients of Taylor coefficients ⋮ On a necessary condition for an entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-Pólya class ⋮ On the closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre-Pólya I class ⋮ On the number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients

Cites Work

• On the zeros of a partial theta function
• On power series having sections with only real zeros
• Complex zero decreasing sequences
• Hardy-Petrovitch-Hutchinson's problem and partial theta function
• On the spectrum of a partial theta function
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