Abstract
We provide a survey of identities for sums of the type \(\sum _{n\leq x}a(n)\log (x/n).\) In each case, a(n) is an arithmetical function generated by a Dirichlet series satisfying a functional equation involving the gamma function. Moreover, all of the identities given in this paper feature infinite series of Bessel functions.
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Berndt, B.C., Kim, S. (2015). Identities for Logarithmic Means: A Survey. In: Alaca, A., Alaca, Ş., Williams, K. (eds) Advances in the Theory of Numbers. Fields Institute Communications, vol 77. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3201-6_1
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DOI: https://doi.org/10.1007/978-1-4939-3201-6_1
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