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The q-pell Hyperbolic Functions |
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PP: 185-191 |
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Author(s) |
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Ayse Nur Guncan,
Seyma Akduman,
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Abstract |
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| In this paper, since the standard hyperbolic functions have countless uses in modern science we present a mathematical
study concerning an extension of the Pell sine and cosine hyperbolic functions. The main properties exhibited by the Pell hyperbolic
functions [3], for which they can be obtained from k-Fibonacci hyperbolic functions when k = 2, are reviewed. The new class of
functions, i.e., the q-analogues of Pell hyperbolic functions, are introduced and defined based on the q-analogues of the Pell numbers
and the q-analogue of the ”Silver ratio”, where module q is a number defined between zero and the unity.A battery of properties is
demonstrated: q-Pell Pythagorean Theorem; q-Pell sum and difference; q-Pell double argument; q-Pell half argument; q-Pell Catalan’s
identity; q-Pell Cassini’s identity and q-Pell d’Ocagne’s identity. |
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