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March 2013 Formal proofs of degree 5 binary BBP-type formulas
Kundle Adegoke
Funct. Approx. Comment. Math. 48(1): 19-27 (March 2013). DOI: 10.7169/facm/2013.48.1.2


We study the analytic behavior of a power series with coefficients containing the von Mangoldt function. In particular, we extend an explicit formula of Hardy and Littlewood for related functions and derive further representation formulas in the unit disk that reveal logarithmic singularities on a dense subset of the unit circle. As an essential tool for proving the square integrability of occurring limit functions together with respective error estimates we contribute a new proof of a Ramanujan-like expansion of an arithmetic function consisting of the von Mangoldt function and the Euler function.


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Kundle Adegoke. "Formal proofs of degree 5 binary BBP-type formulas." Funct. Approx. Comment. Math. 48 (1) 19 - 27, March 2013.


Published: March 2013
First available in Project Euclid: 25 March 2013

zbMATH: 1268.11163
MathSciNet: MR3086957
Digital Object Identifier: 10.7169/facm/2013.48.1.2

Primary: 11Y60
Secondary: 30B99

Keywords: BBP type formulas , digit extraction formulas , polylogarithm constants

Rights: Copyright © 2013 Adam Mickiewicz University


Vol.48 • No. 1 • March 2013
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