Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials
نویسندگان
چکیده
منابع مشابه
Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind
In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...
متن کاملGeneralized Chebyshev polynomials of the second kind
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...
متن کاملFibonacci numbers and orthogonal polynomials
We prove that the sequence (1/Fn+2)n≥0 of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little q-Jacobi polynomials with q = (1− √ 5)/(1+ √ 5). We prove that the corresponding kernel polynomials have integer coefficients, and from this we deduce that the inverse of the corresponding Hankel matrices (1/F...
متن کاملA spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...
متن کاملsecond language acquisition of telicity and aspect by persian learners of english
این تحقیق از دو قسمت اصلی تشکیل شده است: در قسمت اول فراگیری ختمیت به ویژه درک و تولید اینگونه جملات توسط فراگیران ایرانی زبان انگلیسی مورد بررسی قرار گرفته است. قضاوت تعدادی انگلیسی زبان بر روی این جملات نیز هدفی دیگر بود که در این رساله بررسی شده است. از موضوعات دیگر تفاوت بین نشانه های ختمیت در زبان انگلیسی و فارسی و تاثیر زبان اول فراگیران در درک و تولید اینگونه جملات است. در قسمت دوم استفا...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2018
ISSN: 2227-7390
DOI: 10.3390/math6100210