Integral transform with generalized confluent hypergeometric function
The authors introduce the following generalized confluent hypergeometric function: \[ {}_1\Phi_1^{\omega,\mu}(z)= \frac{\Gamma(c)}{\Gamma(a)} \sum_{n=0}^\infty\;\frac{\Gamma[a+(\omega/ \mu)n]z^n}{\Gamma[c+(\omega/ \mu)n]n!} \] and studied some of its important properties. They have also introduced an integral transform with a kernel containing the function \({}_1\Phi_1^{\omega,\mu}(z)\) and established its inversion formula.
scientific article; zbMATH DE number 1051134