Orthogonal Polynomials Related to the Oscillatory-chebyshev Weight Function

نویسندگان

  • G. V. MILOVANOVIĆ
  • A. S. CVETKOVIĆ
  • G. V. Milovanović
  • A. S. Cvetković
چکیده

L(p) = ∫ 1 −1 p(x)x(1− x2)−1/2eiζxdx, ζ ∈ R. Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived. AMS Mathematics Subject Classification (2000): Primary 30C10, 33C47

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

متن کامل

Bivariate Chebyshev-i Weighted Orthogonal Polynomials on Simplicial Domains

We construct a simple closed-form representation of degree-ordered system of bivariate Chebyshev-I orthogonal polynomials Tn,r(u, v, w) on simplicial domains. We show that these polynomials Tn,r(u, v, w), r = 0, 1, . . . , n; n ≥ 0 form an orthogonal system with respect to the Chebyshev-I weight function.

متن کامل

A Family of Generalized Jacobi Polynomials

The family of orthogonal polynomials corresponding to a generalized Jacobi weight function was considered by Wheeler and Gautschi who derived recurrence relations, both for the related Chebyshev moments and for the associated orthogonal polynomials. We obtain an explicit representation of these polynomials, from which the recurrence relation can be derived.

متن کامل

Computation of integrals with oscillatory and singular integrands using Chebyshev expansions

This paper is concerned with evaluation of integrals whose integrands are oscillatory and contain singularities at the endpoints of the interval of integration. A typical form is G(9) ■ f * w(x)e*xf(x) dx, where a and b can be finite or infinite, 9 is a parameter which is usually large, fix) is analytic in the range of integration, and the singularities are encompassed in the weight function w(...

متن کامل

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005