Some relations between Jacobi and ultraspherical polynomials
نویسندگان
چکیده
منابع مشابه
Some relations between Kekule structure and Morgan-Voyce polynomials
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...
متن کاملSome Properties of Jacobi Polynomials
A main motivation for this paper is the search for the sufficient condition of the primality of an integer n in order that the congruence 1n−1 + 2n−1 + 3n−1 + · · · + (n− 1)n−1 ≡ −1 (mod n) holds. Some properties of Jacobi polynomials were investigated using certain Kummer results. Certain properties of Bernoulli polynomials as well as the Staudt–Clausen theorem for prime factors were also used...
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 کاملA new characterization of ultraspherical polynomials
We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on [−1, 1] via the special form of the representation of the derivatives pn+1(x) by pk(x), k = 0, ..., n.
متن کاملUltraspherical Type Generating Functions for Orthogonal Polynomials
We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1981
ISSN: 0022-247X
DOI: 10.1016/0022-247x(81)90204-3