Recently, the parametric kind of some well known polynomials have been presented by many authors. In a sequel of such type of works, in this paper, we introduce the two parametric kinds of degenerate poly-Bernoulli and poly-Genocchi polynomials. Some analytical properties of these parametric polynomials are also derived in a systematic manner. We will be able to find some identities of symmetry for those polynomials and numbers.

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Abstract. In the present paper, we define the generalized extended Whittaker function in terms of generalized extended confluent hypergeometric function of the first kind. We also study its integral representation, some integral transforms and its derivative.

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We introduce a further generalization of the extended Whittaker function by using the generalized extended confluent hypergeometric function of the first kind and investigate, in a rather systematic manner, its integral representations, some integral transforms, differential formula and recurrence relations. Relevant connections of some results presented here with those involving relatively simpler known formulas are also indicated. In view of diverse applications of the Whittaker function in the mathematical physics, the results here may be potentially useful in some related research areas.