摘要
本文研究了在结点系{z_k^(n)=e^(((2k-1)/n)ni)}_(k=1)~n 上关于函数类 A 的 Lagrange 插补多项式的白恩斯坦—罗格辛斯基求和 U_n(f,z)=1/2{Ln(f,ze^(((s)/n)i)+Ln(f,ze^((-(s)/n)i)}在单位闭圆上的发散性与内闭一致收敛性。
Letf ∈A denote f(z)analytic in |z|<1 and continuous on |z|≦1,and z_k=z_k^(n)
=e^(iok).O_k=(2k-1)/nπ.k=1.2.…n. n=1.2.…The corresponding lagrange interpolation
polynomial is Ln(f.z)=sum from k=1 to nf(z_N)L_x(z)
where L_k(z)=w(z)/(z-z_k)w′(z_k).w(z)=multiply from k=1 to n(z-z_k)
Expond Ln(f.z)in the following form: Ln(f.z)=sum from (?) to(n-1)A_(?)(f)z_(?),A(?)(f)=sum from l=1 ton z^jf(z_k)
Define Un(f.z)=1/2{Ln(f.zen/n(?))+Ln(f.ze-n/n(?)}
We have Theoreml Supposef∈A.Then U_n(f.z)converges uniformly tof(z)on arbitrary
closed domain in|z|<1.
Theorem2 Supposef∈A and{p_k^(n)}R=0.Satisfy the condition that Limp_k^(n)=1.
Then Vn(f.z)=sum from j=0 to(?)p_(?)^(n)A_(?)(f)z^J
converges uniformly tof(z) on arbitrary closed doman in|z|<1.
Theorem3 There exists a function f∈A.such that
Lim Un(f.-1)=∞
出处
《河南科学》
1990年第1期1-9,共9页
Henan Science
关键词
LAGRANGE
插补多项式
求和
Function class A(analyric in |Z|<l and conrinuons on |Z|<1)Lagrange interpolation
Bernsteim-Rogosinski Summation
divergence
converge unformly
