The expansion of the confluent hypergeometric function on the positive real axis

Abstract

The asymptotic expansion of the Kummer function ${}_1{F}_1(a;b;z)$ is examined as $z\to +\infty$ on the Stokes line $\arg z=0$. The correct form of the subdominant algebraic contribution is obtained for non-integer $a$. Numerical results demonstrating the accuracy of the expansion are given.

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