A New Proof of a Theorem in Analysis by Generating Integrals and Fractional Calculus

Details A New Proof of a Theorem in Analysis by Generating Integrals and Fractional Calculus A New Proof of a Theorem in Analysis by Generating Integrals and Fractional Calculus

1998-12-26

arxiv.org/abs/math/9812147v1

Mathematics

Classical Analysis and ODEs

14 pages, 2figures, LaTeX, \usepackage[dvips]

Scientific paper

The idea of generating integrals analogous to generating functions is first
introduced in this paper. A new proof of the well-known Finite Harmonic Series
Theorem in Analysis and Analytical Number Theory is then obtained by the method
of Generating Integrals and Fractional Calculus. A generalization of the
Riemann zeta function up to non-integer order is derived.

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