q-Identities from Lagrange and Newton Interpolation

نویسندگان

  • Amy Mei Fu
  • Alain Lascoux
چکیده

Combining Newton and Lagrange interpolation, we give q-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.

برای دانلود رایگان 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

Analysis of Accuracy of Interpolation Methods in Estimating the Output Factors for Square Fields in Medical Linear Accelerator

Introduction: To estimate the accuracy levels of Lagrange, Newton backward interpolation, and linear interpolation methods in estimating the output factors for square fields used in linear accelerator for 6 MV photons at various depths. Materials and Methods: Ionization measurements were carried out in radiation field analyzer in linear accelerator for 6 MV beams at the depths of 5 and 10 cm by...

متن کامل

Rational Interpolation and Basic Hypergeometric Series

We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the recent interpolation formula of Zhi-Guo Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula.

متن کامل

Constant Term Identities and Poincaré Polynomials

In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald’s constant term identities admit an extra set of free parameters, thereby linking them to Poincaré polynomials. We then exploit these extra degrees of freedom in the case of type A to give the first proof of Kadell’s orthogonality ...

متن کامل

Numerische Mathematik Manuscript-nr. Polynomial Interpolation of Minimal Degree

Minimal degree interpolation spaces with respect to a nite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solv-able and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange inter...

متن کامل

On Multivariate Lagrange Interpolation

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002