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2015•Applied Mathematical SciencesOpen access

An explicit formula for generalized arithmetic-geometric sum

Roberto Bagsarsa Corcino, Cristina Bordaje Corcino, Cyril A. Flores

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Abstract

Abstract A short survey on different derivations of the explicit formula for the arithmetic geometric sums and their generalizations is given in the introductory part of the paper. Moreover, an explicit formula for certain generalized arithmetic geometric sums is established using the concept of kth differentiation and Leibniz formula. The formula is expressed in terms of the generalized Eulerian polynomials.

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Abstract A short survey on different derivations of the explicit formula for the arithmetic geometric sums and their generalizations is given in the introductory part of the paper. Moreover, an explicit formula for certain generalized arithmetic geometric sums is established using the concept of kth differentiation and Leibniz formula. The formula is expressed in terms of the generalized Eulerian polynomials.

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Available abstract

Abstract A short survey on different derivations of the explicit formula for the arithmetic geometric sums and their generalizations is given in the introductory part of the paper. Moreover, an explicit formula for certain generalized arithmetic geometric sums is established using the concept of kth differentiation and Leibniz formula. The formula is expressed in terms of the generalized Eulerian polynomials.

Key concepts: Arithmetic, Mathematics, Algebra over a field, Pure mathematics

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