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Power series with skew-harmonic numbers, dilogarithms, and double integrals

In: Tatra Mountains Mathematical Publications, vol. 56, no. 3
Khristo N. Boyadzhiev
Detaily:
Rok, strany: 2013, 93 - 108
Kľúčové slová:
harmonic numbers, skew-harmonic numbers, dilogarithm, trilogarithm, double integrals.
O článku:
The skew-harmonic numbers are the partial sums of the alternating harmonic series, i.e., the expansion of log 2. We evaluate in closed form various power series and numerical series with skew-harmonic numbers. This provides a simultaneous solution of two recent problems by Ovidiu Furdui in the American Mathematical Monthly and the College Mathematics Journal. We also present and discuss representations involving the dilogarithm and the trilogarithm which are related to our results. Finally, we provide the evaluations of several double integrals in terms of classical constants.
Ako citovať:
ISO 690:
Boyadzhiev, K. 2013. Power series with skew-harmonic numbers, dilogarithms, and double integrals. In Tatra Mountains Mathematical Publications, vol. 56, no.3, pp. 93-108. 1210-3195.

APA:
Boyadzhiev, K. (2013). Power series with skew-harmonic numbers, dilogarithms, and double integrals. Tatra Mountains Mathematical Publications, 56(3), 93-108. 1210-3195.