Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Summability of Jacobi series

Author: Richard Askey
Journal: Trans. Amer. Math. Soc. 179 (1973), 71-84
MSC: Primary 42A56; Secondary 33A65
MathSciNet review: 0315351
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The positivity of some Cesàro mean is proven for Jacobi series $ \Sigma {a_n}P_n^{(\alpha ,\beta )}(x),\alpha ,\beta \geqq - \tfrac{1}{2}$. This has applications to the mean convergence of Lagrange interpolation at the zeros of Jacobi polynomials. The positivity of the $ (C,\alpha + \beta + 2)$ means is conjectured and proven for some $ (\alpha ,\beta )$. One consequence of this conjecture would be the complete monotonicity of $ {x^{ - c}}{({x^2} + 1)^{ - c}},c \geqq 1$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42A56, 33A65

Retrieve articles in all journals with MSC: 42A56, 33A65

Additional Information

PII: S 0002-9947(1973)0315351-7
Keywords: Positive Cesàro sum, Jacobi polynomial, Bessel function, Poisson kernel, delayed means, Lagrange interpolation
Article copyright: © Copyright 1973 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia