• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1179-1192
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• 2018

Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1055-1073
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• 2018

In this paper, we define an alternative q-analogue of the $Ruci{\acute{n}}ski$-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be q-deformations of similar properties for the $Ruci{\acute{n}}ski$-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of A-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the $Ruci{\acute{n}}ski$-Voigt and the q-$Ruci{\acute{n}}ski$-Voigt numbers.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.611-623
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• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.315-326
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• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.