Jacobi Polynomials and Congruences Involving Some Higher-Order Catalan Numbers and Binomial Coefficients

被引：0

作者：

Pilehrood, Khodabakhsh Hessami ^{[1
]}

Pilehrood, Tatiana Hessami ^{[1
]}

机构：

[1] Fields Inst Res Math Sci, 222 Coll St, Toronto, ON M5T 3J1, Canada

来源：

JOURNAL OF INTEGER SEQUENCES | 2015年 / 18卷 / 11期

关键词：

Jacobi polynomial; higher-order Catalan number; polynomial congruence; cubic residue; generating function;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study congruences on sums of products of binomial coefficients that can be proved by using properties of the Jacobi polynomials. We give special attention to polynomial congruences containing Catalan numbers, second-order Catalan numbers, the sequence S-n = [GRAPHICS] , and the binomial coefficients [GRAPHICS] and [GRAPHICS] . As an application, we address several conjectures of Z. W. Sun on congruences of sums involving S-n and we prove a cubic residuacity criterion in terms of sums of the binomial coefficients [GRAPHICS] conjectured by Z. H. Sun.

引用

页数：38