Kunle Adegoke
Abstract
In this paper, direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. The high point of the paper is the discovery of certain combinations of Euler sums that are reducible to Riemann zeta values.
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In this paper, direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. The high point of the paper is the discovery of certain combinations of Euler sums that are reducible to Riemann zeta values.
Key concepts: Harmonic number, Euler's formula, Mathematics, Series (stratigraphy), Proof of the Euler product formula for the Riemann zeta function, Riemann hypothesis, Euler summation, Euler number (physics)