Abstract:
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.
