Some sums of Legendre and Jacobi polynomials
نویسندگان
چکیده
منابع مشابه
Some 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 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 Experiments with Evaluation of Legendre Polynomials
Common practice is to recommend evaluation of polynomials by Horner’s rule. Here’s an example where it is fast but doesn’t work nearly as accurately as another fairly easy method. Can a method for Legendre polynomials be both fast and accurate? 1 1 Legendre Polynomials A substantial literature has grown up around the uses for orthonormal polynomials. Here we look at the example of Legendre poly...
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 کاملOn some special Legendre sums of the form
We prove that sums of the form S = p−1 ∑ x=0 ( g(x) p ) f(x) with f(X), g(X) ∈ Z[X] can be explicitly computed whenever f and g are subject to some certain conditions which are defined in the paper.
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: Mathematica Bohemica
سال: 2001
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2001.133910