Some new properties of Confluent Hypergeometric Functions

Xu-Dan Luo, Wei-Chuan Lin

The confluent hypergeometric functions (the Kummer functions) defined by ${}_1{F}_1(\alpha ;\gamma ;z):={\sum }_{n=0}^{\infty }\frac{(\alpha {)}_n}{n!(\gamma {)}_n}{z}^n(\gamma \ne 0,-1,-2,\cdots )$, which are…