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On (ρ,q)-Euler numbers and polynomials associated with (ρ,q)-Volkenborn integrals

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Recently, Araci et al. introduced (ρ,q)-analogue of the Haar distribution and by means of the distribution, they constructed (ρ,q)-Volkenborn integral yielding to Carlitz’s-type (ρ,q)-Bernoulli numbers and polynomials. The aim of… Click to show full abstract

Recently, Araci et al. introduced (ρ,q)-analogue of the Haar distribution and by means of the distribution, they constructed (ρ,q)-Volkenborn integral yielding to Carlitz’s-type (ρ,q)-Bernoulli numbers and polynomials. The aim of the present paper is to introduce a generalization of the fermionic p-adic measure based on (ρ,q)-integers and set the corresponding integral to this measure. Consequently, Carlitz’s-type (ρ,q)-Euler polynomials and numbers are defined in terms of the above mentioned integral. Moreover, some of their identities and properties are established.

Keywords: numbers polynomials; volkenborn integrals; polynomials associated; associated volkenborn; euler numbers

Journal Title: International Journal of Number Theory
Year Published: 2018

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