ON ARITHMETIC FUNCTIONS, THEIR EXTENDED COEFFICIENTS: VARIOUS RESULTS AND RELATIONS
By
Hemant Kumar1, R. C. Singh Chandel2 and J. Lopez-Bonilla3
1Department of Mathematics, D. A-V. Postgraduate College Kanpur, Uttar Pradesh, India-208001
2Former Head, Department of Mathematics, D. V. Postgraduate College Orai, Uttar Pradesh, India-285001
3ESIME-Zacatenco, Instituto Politecnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP, CDMX, Mexico-07738
Email: palhemant2007@rediffmail.com, rc_chandel@yahoo.com, jlopezb@ipn.mx
(Received: September 27, 2023; In format: October 10, 2023; Revised October 24, 2023; Accepted: October 31, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53225
Abstract
In this article, we represent a recurrence relation of the arithmetic function connected with an ascending factorial function, Lah and Stirling numbers. We then obtain a relation of harmonic numbers and again extend the coecients of these arithmetic functions involving Bell polynomials through introducing the sequence of Hankel type integrals. On the other hand, making some of the extensions of these arithmetic functions, we derive some more results and the summation formulae in terms of Riemann Zeta function.
2020 Mathematical Sciences Classification: 05A19; 11B65; 11B73
Keywords and Phrases: Partial Bell polynomial, Lah and Stirling numbers, Arithmetic functions, Harmonic numbers, Sequence of Hankel integrals, Generating functions.