𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the positivity of ultraspherical type quadrature formulas with Jacobi abscissas

✍ Scribed by G. Sottas

Publisher
Springer
Year
1989
Tongue
English
Weight
674 KB
Volume
38
Category
Article
ISSN
0001-9054

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Interpolatory quadrature formulae with C
Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind
✍ Sotirios E. Notaris πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 755 KB

We consider interpolatory quadrature formulae, relative to the Legendre weight function on [-1, 1], having as nodes the zeros of the nth-degree Chebyshev polynomial of the third or fourth kind. Szeg5 has shown that the weights of these formulae are all positive. We derive explicit formulae for the w

New quadrature formulas based on the zer
New quadrature formulas based on the zeros of Jacobi polynomials
✍ A.K. Varma; E. Landau πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 364 KB

The main object of this paper is to construct a new quadrature formula based on the zeros of the polynomial (1 -x2)P(a'f~)(x)P(a'B)' (x), where P(a'f~)(x) is the Jacobi polynomial of degree n. It is interesting to mention that this quadrature formula is closely related to the wellknown Gaussian Quad

Birkhoff quadrature formulae based on th
Birkhoff quadrature formulae based on the zeros of Jacobi polynomials
✍ M. LΓ©naΓ‘rd πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 549 KB

The main object of this paper is to construct a Birkhoff quadrature formula of the form which is exact for the polynomials of degree < 2n + 2k + 1. We construct the formula when the nodes {Xi}; and {zt}F-' are the zeros of the ultraspherical polynomials P~k'(z) and P,$""(z), respectively.