多元米塔格-莱夫勒函数的积分表示与渐近行为
Integral representations and asymptotic behaviors of the Multivariate Mittag-Leffler function
浏览论文内容
中文总结 AI 辅助
研究多元米塔格-莱夫勒函数，基于倒数伽马函数的汉克尔积分表示及围道变换，推导其积分表示与渐近展开，扩展了单变量和双变量函数的已知结果，为含多分数阶导数的方程定性分析提供工具。
中文摘要 AI 辅助
本文研究了在具有多个分数阶参数的分数阶微分方程理论中出现的多元米塔格-莱夫勒型函数。推导了三变量米塔格-莱夫勒函数新的汉克尔围道积分表示，并在复平面的不同扇形区域建立了完整的渐近展开。该方法基于倒数伽马函数的经典汉克尔积分表示及合适的围道变换。还为任意变量数的多元米塔格-莱夫勒函数建立了相应积分表示和渐近展开，扩展了已知单变量和双变量函数的结果，为含多个分数阶导数的分数阶微分方程定性分析提供工具。
英文摘要
In this paper, a multivariate Mittag--Leffler-type function arising in the theory of fractional differential equations with several fractional parameters is investigated. New Hankel contour integral representations are derived for the three-variable Mittag--Leffler function, and complete asymptotic expansions are established in different sectors of the complex plane. The proposed approach is based on the classical Hankel integral representation of the reciprocal Gamma function together with suitable contour transformations. Furthermore, the corresponding integral representations and asymptotic expansions are established for the multivariate Mittag-Leffler function with an arbitrary number of variables. The obtained formulas extend several known results for one- and two-variable Mittag--Leffler functions and provide useful analytical tools for the qualitative analysis of fractional differential equations involving multiple fractional derivatives.
