The trigonometry of numbers (Q2531334)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The trigonometry of numbers |
scientific article |
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The trigonometry of numbers (English)
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1968
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Series representations are derived for the logarithm, exponential, \(r\)th power and trigonometric operators introduced recently by the author [Duke Math. J. 35, 761--766 (1968; Zbl 0169.37201)]. These ``arithmetic power series'' are fairly similar in form and behavior to their counter-parts in ordinary analysis. They are used as generating functions to obtain identities for a generalized binomial coefficient which appears in the series for \(f^r\). A new formula for the Möbius function arises by taking \(f(n)\) to be identically 1 in the series for \(f^{-1}\).
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nonlinear operators on arithmetic functions
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series representations
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logarithm operator
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exponential operator
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\(r\)th power operator
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trigonometric operator
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generating functions
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identities for generalized binomial coefficient
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Möbius function
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