A Connection Formula for the q-Confluent Hypergeometric Function

Abstract

We show a connection formula for the q-confluent hypergeometric functions ₂φ₁(a,b;0;q,x). Combining our connection formula with Zhang's connection formula for ₂φ₀(a,b;−;q,x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit q→1− of our connection formula.