Zeros of Gegenbauer and Hermite polynomials and connection coefficients

نویسندگان

  • Iván Area
  • Dimitar K. Dimitrov
  • Eduardo Godoy
  • André Ronveaux
چکیده

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

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

A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions

A Maple algorithm for the computation of the zeros of orthogonal polynomials (OPs) and special functions (SFs) in a given interval [x1, x2] is presented. The program combines symbolic and numerical calculations and it is based on fixed point iterations. The program uses as inputs the analytic expressions for the coefficients of the three-term recurrence relation and a differencedifferential rel...

متن کامل

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, ...

متن کامل

Operational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...

متن کامل

ON THE EQUATION OF THE p -ADIC OPEN STRING FOR THE SCALAR TACHYON FIELD

We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the p-adic open string for the scalar tachyon field p 1 2 ∂ t Φ = Φ. We elicit the role of real zeros of the entire function Φ(z) and the behaviour of solutions Φ(t) in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if p is even. We...

متن کامل

Zeros of Sobolev Orthogonal Polynomials of Gegenbauer Type

where l > 0 and {dk0, dk1} is a so-called symmetrically coherent pair, with dk0 or dk1 the classical Gegenbauer measure (x−1) dx, a > −1. If dk1 is the Gegenbauer measure, then Sn has n different, real zeros. If dk0 is the Gegenbauer measure, then Sn has at least n−2 different, real zeros. Under certain conditions Sn has complex zeros. Also the location of the zeros of Sn with respect to Gegenb...

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:
  • Math. Comput.

دوره 73  شماره 

صفحات  -

تاریخ انتشار 2004