Resurgence in the Transition Region: The Incomplete Gamma Function

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Nemes, Gergő
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212169
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Resurgence in the Transition Region: The Incomplete Gamma Function. Gergő Nemes. SIGMA 20 (2024), 026, 14 pages

We study the resurgence properties of the coefficients ₙ() appearing in the asymptotic expansion of the incomplete gamma function within the transition region. Our findings reveal that the asymptotic behaviour of ₙ() as → +∞ depends on the parity of . Both ₂ₙ₋₁() and ₂ₙ(τ) exhibit behaviours charac...