论文标题
$ a \ to a \ 1 $时，MITTAG-LEFFLER函数的渐近函数$ e_a（z）$
Asymptotics of the Mittag-Leffler function $E_a(z)$ on the negative real axis when $a\to 1$
论文作者
论文摘要
我们将单参数Mittag-Leffler函数的渐近扩展$ e_a（-x）$ for $ x \ to+\ to+\ infty $作为参数$ a \ to1 $。 $ 0 <a <1 $的主要扩展由代数扩展为$ o（x^{ - 1}）$（当$ a = 1 $时消失），以及接近$ e^{ - x} $ as $ a \ a \ to 1 $的$ e^{ - x} $。在这里，当$ a $接近价值1时，我们专注于这种指数小的扩展形式。 提出了数值示例，以说明所获得的扩展的准确性。
We consider the asymptotic expansion of the single-parameter Mittag-Leffler function $E_a(-x)$ for $x\to+\infty$ as the parameter $a\to1$. The dominant expansion when $0<a<1$ consists of an algebraic expansion of $O(x^{-1})$ (which vanishes when $a=1$), together with an exponentially small contribution that approaches $e^{-x}$ as $a\to 1$. Here we concentrate on the form of this exponentially small expansion when $a$ approaches the value 1. Numerical examples are presented to illustrate the accuracy of the expansion so obtained.
