Article
New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers
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Abstract
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both finite and infinite sums. The high points of this paper are the discovery of several previously unknown infinite summation results involving non-linear generalized harmonic number terms and the derivation of interesting alternating summation formulas involving these numbers.
Keywords
harmonic numbers, Riemann zeta function, polygamma function, polylogarithm function, Bernoulli number, Euler number, summation identity
Citation
Adegoke, K. & Layeni, O. (2016). New finite and infinite summation identities involving the generalized harmonic numbers. Journal of Analysis & Number Theory, 4(1), 49–60. https://doi.org/10.18576/jant/040108
K. Adegoke and O. Layeni, “New finite and infinite summation identities involving the generalized harmonic numbers,” Journal of Analysis & Number Theory, vol. 4, no. 1, pp. 49–60, 2016, doi: 10.18576/jant/040108.
Adegoke K, Layeni O. New finite and infinite summation identities involving the generalized harmonic numbers. Journal of Analysis & Number Theory. 2016;4(1):49–60. doi:10.18576/jant/040108.
Adegoke, K. and Layeni, O. (2016), ‘New finite and infinite summation identities involving the generalized harmonic numbers’, Journal of Analysis & Number Theory, 4(1), pp. 49–60. Available at: https://doi.org/10.18576/jant/040108.
Adegoke, Kunle, and Olawanle Layeni. “New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers.” Journal of Analysis & Number Theory, vol. 4, no. 1, 2016, pp. 49–60. https://doi.org/10.18576/jant/040108.
Adegoke, Kunle, and Olawanle Layeni. “New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers.” Journal of Analysis & Number Theory 4, no. 1 (2016): 49–60. https://doi.org/10.18576/jant/040108.
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Published by: Engineering Journals


