(ρ,q)-Volkenborn integration
By Serkan Araci, U. Duran, Mehmet Acikgoz. 2017
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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.
Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2f40da8efdbf0e5b98e02d11ceb9b216c4528e99
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In Algebra and Number Theory
In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Explicit formulas for p-adic integrals: approach to p-adic distributions and some families of special numbers and polynomials. (2019, methodology): “[101]; see also [57], [59] and the references cited in each of these earlier works).”