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In the present paper, unification of Bessel, modified Bessel, sphericalBessel and Bessel-Clifford functions via the generalized Pochhammer symbol [Srivastava HM, Cetinkaya A, K{\i}ymaz O. A certain generalized Pochhammersymbol and its applications to hypergeometric functions. Applied Mathematicsand Computation, 2014, 226 : 484-491] is defined. Several potentially usefulproperties of the unified family such as generating function, integralrepresentation, Laplace transform and Mellin transform are obtained. Besides,the unified Bessel, modified Bessel, spherical Bessel and Bessel-Cliffordfunctions are given as a series of Bessel functions. Furthermore, thederivatives, recurrence relations and partial differential equation of theso-called unified family are found. Moreover, the Mellin transform of theproducts of the unified Bessel functions are obtained. Besides, a three-foldintegral representation is given for unified Bessel function. Some of theresults which are obtained in this paper are new and some of them coincide withthe known results in special cases.

Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions