Two new conjectures concerning positive Jacobi polynomials sums
نویسندگان
چکیده
A refinement of a conjecture of Gasper concerning the values of (α, β), −1/2 < β < 0, −1 < α + β < 0, for which the inequalities
منابع مشابه
Two New Conjectures concerning Positive Jacobi Polynomial Sums
A reenement of a conjecture of Gasper concerning the values
متن کاملExtended Jacobi and Laguerre Functions and their Applications
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...
متن کاملZeros and orthogonality of the Askey-Wilson polynomials for q a root of unity
We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive Nth root of unity. For general four-parameter AWP, zeros of the Nth polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval i...
متن کاملPositivity of certain sums over Jacobi kernel polynomials
We present a computer-assisted proof of positivity of sums over kernel polynomials for ultraspherical Jacobi polynomials.
متن کاملSome Sums of Legendre and Jacobi Polynomials
We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.
متن کاملذخیره 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