ON ARITHMETIC FUNCTIONS, THEIR EXTENDED COEFFICIENTS: VARIOUS RESULTS AND RELATIONS

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.