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On four families of power series involving harmonic numbers and central binomial coefficients
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We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate different families of power series which involve odd harmonic numbers and central binomial coefficients. Furthermore it is shown that based on these series a new type of nonlinear Euler sums that involve odd harmonic numbers can be calculated in terms of zeta functions.
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On an infinite number of nonlinear Euler sums
Eight families of quadratic Euler sums of odd order are reduced to zeta values and polylogarithms, but order-7 reductions remain incomplete for two unresolved nonlinear sums.
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