Complex Appell–Bessel Functions and Their Degenerate Analogs

In this article, a family of complex Appell–Bessel functions is considered and an integral representation for this family is derived. As a consequence, cosine and sine analogs of these functions are obtained. Certain properties, including addition formulas and differential recurrence relations, are also established. Further, the degenerate complex Appell–Bessel functions are investigated, and certain results for degenerate cosine-Appell–Bessel and degenerate sine-Appell–Bessel functions are obtained. Jacobi–Anger expansions for complex Appell–Bessel functions and degenerate complex Appell–Bessel functions are explored as well.