# Tricomi confluent hypergeometric function

Let $$U(\alpha,\delta,z)=\frac{\Gamma(1-\delta)}{\Gamma(\alpha-\delta+1} {}_1\!F_1(\alpha,\delta,z) + z^{1-\delta}\frac{\Gamma(\delta-1)}{\Gamma(\delta)}\!F_1(\alpha-\delta+1, 2-\delta,z)$$ be the Tricomi confluent hypergeometric function. the function $$a\to U(a,1,z)$$ is it holomorphic on $$C$$?

• – gammatester Nov 8 '18 at 21:41
• Thanks a lot you. Have you other references? – Kacdima Nov 8 '18 at 22:09