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A New Formula for the Natural Logarithm of a Natural Number

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Abstract

For every natural number T, we write \(\mathrm{Ln }\,T\) as a series, generalizing the known series for \(\mathrm{Ln }\,2.\) We also introduce related linear subspaces of \(\mathbb{C }\).

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References

  1. Eymard, P., Lafon, J.-P.: The Number \(\pi \). American Mathematical Society, Providence (2004)

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  2. Mascheroni, L.: Adnotationes ad Calculum Integralem Euleri, Vol. 1 and 2, Ticino, Italy, 1790 and 1792 (Reprinted in L. Euler, Leonhardi Euleri Opera Omnia, Ser. 1, Vol. 12, Leipzig, Germany: Teubner, pp. 415–542, 1915)

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Acknowledgments

The author thanks the anonymous referee for his very valuable suggestions that resulted in a significant improvement of the paper.

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Correspondence to Shahar Nevo.

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Communicated by Stephan Ruscheweyh.

This research is supprted by the Israel Science Foundation, Grant No. 395/07.

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Nevo, S. A New Formula for the Natural Logarithm of a Natural Number. Comput. Methods Funct. Theory 13, 153–161 (2013). https://doi.org/10.1007/s40315-013-0012-4

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  • DOI: https://doi.org/10.1007/s40315-013-0012-4

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