Asymptotics of some generalized Mathieu series

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F20%3AA2102942" target="_blank" >RIV/61988987:17310/20:A2102942 - isvavai.cz</a>
Result on the web
<a href="https://www.mscand.dk/article/view/121106" target="_blank" >https://www.mscand.dk/article/view/121106</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7146/math.scand.a-121106" target="_blank" >10.7146/math.scand.a-121106</a>

Result language
angličtina
Original language name
Asymptotics of some generalized Mathieu series
Original language description
We establish asymptotic estimates of Mathieu-type series defined by sequences with power-logarithmic or factorial behavior. By taking the Mellin transform, the problem is mapped to the singular behavior of certain Dirichlet series, which is then translated into asymptotics for the original series. In the case of power-logarithmic sequences, we obtain precise first order asymptotics. For factorial sequences, a natural boundary of the Mellin transform makes the problem more challenging, but a direct elementary estimate gives reasonably precise asymptotics. As a byproduct, we prove an expansion of the functional inverse of the gamma function at infinity.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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