Integral Relations between the k-Function with Non-Integral Index and Confluent Hypergeometric Functions

In a recent paper some properties of the k-function with non-integral index were established by the author. It is the object of this note to connect this function with Whittaker's function and its particular cases like Sonine's Polynomial, the Incomplete Gamma-function and the Pearson-Cunningham function. Incidentally, as will be seen, we get an integral equation for the k-function.