1. Basics of Multiple Polyexponential Integrals
- Author
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Aminov, Gleb and Arnaudo, Paolo
- Subjects
Mathematics - Classical Analysis and ODEs ,General Relativity and Quantum Cosmology ,High Energy Physics - Theory ,Mathematical Physics - Abstract
We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of second-order ODEs around an irregular singularity. In particular, their recursive definition describes the asymptotic behavior of these local solutions. To complement the study of the multiple polyexponential integrals on the entire complex plane, we relate them with two other sets of special functions - the undressed and dressed multiple polyexponential functions - which are characterized by their Taylor series expansions around the origin., Comment: Version 2, some references were added, 47 pages
- Published
- 2024