Functiones et Approximatio Commentarii Mathematici

Formal proofs of degree 5 binary BBP-type formulas

Kundle Adegoke

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Abstract

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.

Article information

Source
Funct. Approx. Comment. Math., Volume 48, Number 1 (2013), 19-27.

Dates
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1364222826

Digital Object Identifier
doi:10.7169/facm/2013.48.1.2

Mathematical Reviews number (MathSciNet)
MR3086957

Zentralblatt MATH identifier
1268.11163

Subjects
Primary: 11Y60: Evaluation of constants
Secondary: 30B99: None of the above, but in this section

Keywords
BBP type formulas digit extraction formulas polylogarithm constants

Citation

Adegoke, Kundle. Formal proofs of degree 5 binary BBP-type formulas. Funct. Approx. Comment. Math. 48 (2013), no. 1, 19--27. doi:10.7169/facm/2013.48.1.2. https://projecteuclid.org/euclid.facm/1364222826


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