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Date: 25-5-2019
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Date: 30-3-2019
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Date: 4-1-2016
2049
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The exponential function has two different natural -extensions, denoted and . They are defined by
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(Koekoek and Swarttouw 1998, p. 18), where is a q-hypergeometric function.
has the special form
(6) |
for .
The -exponential functions are related to the q-cosine and q-sine by
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(8) |
REFERENCES:
Koekoek, R. and Swarttouw, R. F. "The q-Gamma Function and the q-Binomial Coefficient." §0.3 in The Askey-Scheme of Hypergeometric Orthogonal Polynomials and its q-Analogue. Delft, Netherlands: Technische Universiteit Delft, Faculty of Technical Mathematics and Informatics Report 98-17, pp. 18-19, 1998.
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