Some results about Mittag-Leffler function's integral representations
Yayun Wu, Zhihua Liu
TL;DR
This paper investigates the conditions under which Mittag-Leffler functions can be expressed as integrals at the origin, providing proofs and generalizations of key properties.
Contribution
It establishes applicable conditions for integral representations of Mittag-Leffler functions and generalizes important existing results.
Findings
Derived conditions for integral expressions at the origin
Proved new properties of Mittag-Leffler functions
Extended previous results to broader cases
Abstract
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we also generalize some important conclusions about Mittag-Leffler function.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Mathematical Analysis and Transform Methods