Jacobi’s generating function for Jacobi polynomials
نویسندگان
چکیده
منابع مشابه
Generating Functions of Jacobi Polynomials
Multiplicative renormalization method (MRM) for deriving generating functions of orthogonal polynomials is introduced by Asai–Kubo– Kuo. They and Namli gave complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−κ. In this paper, MRM-factors h(x) for which the beta distribution B(p, q) over [0, 1] is MRM-applicable are determined. In other words, all generating function...
متن کاملGenerating function polynomials for legendrian links
It is shown that, in the 1{jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1{jet of the 0{function, and thus cannot be distinguished by the classical rotation number or Thurston{Bennequin invariants. The links are distin...
متن کاملOn mixed trilateral generating functions of extended Jacobi polynomials
In this note we have obtained some novel result on mixed trilateral relations involving extended Jacobi polynomials by group theoretic method which inturn yields the corresponding results involving Hermite, Laguerre and Jacobi polynomials.
متن کاملThe number of convex polyominoes and the generating function of Jacobi polynomials
Lin and Chang gave a generating function of convex polyominoes with an m+1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m+ n+mn m+ n ( 2m+ 2n 2m ) − 2mn m+ n ( m+ n m )2 . We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials. Some (binomia...
متن کاملLocal Estimates for Jacobi Polynomials
It is shown that if α, β ≥ − 12 , then the orthonormal Jacobi polynomials p (α,β) n fulfill the local estimate |p n (t)| ≤ C(α, β) ( √ 1− x+ 1 n ) α+ 2 ( √ 1 + x+ 1 n ) β+ 2 for all t ∈ Un(x) and each x ∈ [−1, 1], where Un(x) are subintervals of [−1, 1] defined by Un(x) = [x− φn(x) n , x+ φn(x) n ]∩[−1, 1] for n ∈ N and x ∈ [−1, 1] with φn(x) = √ 1− x2+ 1 n . Applications of the local estimate ...
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: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0486693-x