2015
DOI: 10.1007/s11785-015-0503-6
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An Extension of the Chebyshev Polynomials

Abstract: Our consideration is focused on determining properties of generalized Chebyshev polynomials of the first and second kind, sparking interest in constructing a theory similar to the classical one. This studies highlight some important results and connections between this two types. The paper is also concerned with the connection between orthogonal polynomials and typically real function, both strictly related to the Koebe function.

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Cited by 4 publications
(1 citation statement)
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“…The celebrated Chebyshev polynomials have a wide range of applications in many fields such as numerical analysis, differential equations, approximation theory, and number theory (see, e.g., [2,9,6]). Some extensions and recent developments of the Chebyshev polynomials can be found, e.g., in [17,8,5,12,11,7,10]. As is well known, the Chebyshev polynomials of the first kind are defined by the recurrence relation T 0 (t) = 1, T 1 (t) = t, T k+1 (t) = 2tT k (t) − T k−1 (t) k = 1, 2, .…”
Section: Introductionmentioning
confidence: 99%
“…The celebrated Chebyshev polynomials have a wide range of applications in many fields such as numerical analysis, differential equations, approximation theory, and number theory (see, e.g., [2,9,6]). Some extensions and recent developments of the Chebyshev polynomials can be found, e.g., in [17,8,5,12,11,7,10]. As is well known, the Chebyshev polynomials of the first kind are defined by the recurrence relation T 0 (t) = 1, T 1 (t) = t, T k+1 (t) = 2tT k (t) − T k−1 (t) k = 1, 2, .…”
Section: Introductionmentioning
confidence: 99%