Gordon Function

Another name for the Confluent Hypergeometric Function of the Second Kind, defined by

$G(a\vert c\vert z)=e^{i\pi a}{\Gamma(c)\over\Gamma(a)}\left\{{{\Gamma(1-c)\over\Gamma(1-a)}\left[{e^{-\pi c}+{\sin[\pi(a-c)]\over\sin(\pi a)}}\right]}\right.$
$\mathop\times\!\left.{{}_1F_1(a;c;z)-2{\Gamma(c-1)\over\Gamma(c-a)} z^{1-c} {}_1F_1(a-c+1;2-c;z)}\right\},$

where $\Gamma(x)$ is the Gamma Function and ${}_1F_1(a;b;z)$ is the Confluent Hypergeometric Function of the First Kind.

See also Confluent Hypergeometric Function of the Second Kind

References

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 671-672, 1953.