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61.
本文给出了基于xL（a）n－1（x）之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中xL（a）n－1（x）为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ0（ｘ）＋Ｃｆ1（ｘ）这里Ｃ为任意常数。 相似文献
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1. Introduction and Main ResultsDenote by Pn the set of algebraic polynomials of degree not exceeding n. LetX = {X = (xl,xz,...,x.). 1 = xl > xz >' > xtL--l > xtL = --l}, n 2 2and let for X E X.Erd6s in [21 raised the question of determining Y E X such thatReceived July 21, 1999.also conjectured that Y = Z satisfyingw,,(Z, x) = c1' l" Pt.--1 (x) dx,j-- 1 Pt.-- 1 (x) dx,1 .2>where P,--1 stands for the (n -- 1)th Legendre polynomial normalized by Pn--1 (1) = l. Thiscolljecture was di… 相似文献