A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
نویسندگان
چکیده
منابع مشابه
Characterization of the generalized Chebyshev-type polynomials of first kind
Orthogonal polynomials have very useful properties in the mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize a sequence of the generalized Chebyshev-type polynomials of the first kind { T (M,N) n (x) } n∈N∪{0} , which are orthogonal with respect to the measure √ 1−x2 π dx + Mδ−1 + Nδ1, w...
متن کاملApplication 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 کاملA new characterization of ultraspherical polynomials
We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on [−1, 1] via the special form of the representation of the derivatives pn+1(x) by pk(x), k = 0, ..., n.
متن کاملSolving Differential Equations by Using a Combination of the First Kind Chebyshev Polynomials and Adomian Decomposition Method
In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method
متن کاملA New Kind of Deformed Hermite Polynomials and Its Applications ∗
A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. As its applications, we calculate e...
متن کاملذخیره 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: Journal of Mathematical Analysis and Applications
سال: 2017
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.11.053