caa a22 4500 60549696X CHVBK 20210128100539.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0520-2 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0520-2 Smith H. Quadrature Research Centre, 2 Valleyfield Park, Terregles, DG2 9RA, Dumfries, Scotland, UK aut Convergence properties of a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function [Elektronische Daten] [H. Smith] A quadrature formula of Clenshaw-Curtis type for functions of the form $$(1-x^2)^{\lambda - \frac{1}{2}}f(x)$$ ( 1 - x 2 ) λ - 1 2 f ( x ) over the interval [ $$-$$ - 1,1] exhibits a curious phenomenon when applied to certain analytic functions. As the number of points in the quadrature rule increases the error may sometimes decay to zero in two distinct stages rather than in one depending on the value of $$\lambda $$ λ . In this paper we shall derive explicit and asymptotic error formulae which describe this phenomenon. Springer Science+Business Media Dordrecht, 2014 Gegenbauer weight function nationallicence Clenshaw-Curtis quadrature nationallicence Convergence rate nationallicence Lobatto-Chebyshev quadrature nationallicence BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 823-842 0006-3835 55:3<823 2015 55 10543 https://doi.org/10.1007/s10543-014-0520-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0520-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Smith H. Quadrature Research Centre, 2 Valleyfield Park, Terregles, DG2 9RA, Dumfries, Scotland, UK aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 823-842 0006-3835 55:3<823 2015 55 10543