Zero distribution and division results for exponential polynomials

2018 ◽  
Vol 227 (1) ◽  
pp. 397-421 ◽  
Author(s):  
Janne Heittokangas ◽  
Katsuya Ishizaki ◽  
Kazuya Tohge ◽  
Zhi-Tao Wen
Keyword(s):  
Exponential Polynomials ◽  
Zero Distribution

scholarly journals An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Ying Wang ◽  
Baodong Zheng ◽  
Chunrui Zhang
Keyword(s):  
Dynamic Systems ◽  
Real Coefficient ◽  
Coupled Systems ◽  
Decomposition Technique ◽  
Exponential Polynomials ◽  
Basic Theorem ◽  
Algebraic Criterion ◽  
The Stability

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

scholarly journals On similarities between exponential polynomials and Hermite polynomials

2013 ◽  
Vol 12 (3) ◽  
pp. 93-104 ◽  
Author(s):  
Edyta Hetmaniok ◽  
◽  
Mariusz Pleszczynski ◽  
Damian Slota ◽  
Roman Witula ◽  
...  
Keyword(s):  
Hermite Polynomials ◽  
Exponential Polynomials

scholarly journals A Note on a Triple Integral

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2056
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Polynomial Functions ◽  
Fundamental Constants ◽  
Form Expression ◽  
Zero Distribution ◽  
Special Cases ◽  
Almost All

A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic, exponential, quotient radical, and polynomial functions. Special cases are derived in terms of fundamental constants; results are summarized in a table. All results in this work are new.

scholarly journals The Diophantine problem for rings of exponential polynomials

2021 ◽  
pp. 8
Author(s):  
Dimitra Chompitaki ◽  
Natalia Garcia-Fritz ◽  
Hector Pasten ◽  
Thanases Pheidas ◽  
Xavier Vidaux
Keyword(s):  
Exponential Polynomials ◽  
Diophantine Problem
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