1. (ρ,q)-Volkenborn integration.
- Author
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Araci, Serkan, Duran, Ugur, and Acikgoz, Mehmet
- Subjects
- *
INTEGRALS , *DISTRIBUTION (Probability theory) , *GENERALIZATION , *POLYNOMIALS , *DERIVATIVES (Mathematics) - Abstract
In the paper, we introduce an analogue of Haar distribution based on ( ρ , q ) -numbers, as follows: μ ρ , q ( a + p N Z p ) = ρ p N [ p N ] ρ , q ( q ρ ) a . By means of this distribution, we derive ( ρ , q ) -analogue of Volkenborn integration which is a new generalization of Kim's q -Volkenborn integration defined in [11] . From this definition, we investigate some properties of Volkenborn integration based on ( ρ , q ) -numbers. Finally, we construct ( ρ , q ) -Bernoulli numbers and polynomials derived from ( ρ , q ) -Volkenborn integral and obtain some their properties. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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