求解:
(1)用b(1),b(2)……表示出Bell多项式系数B(7,n)(b)(n从1到7)
(2)若b(k)=1/k;任意整数m,求证
sigma B(m,n)(b)/n! =1 (n from 1 to m)
f(x)在[0,1]上连续且恒正,
integrate f(x) from 0 to 1 = 2019
integrate f(x)^2 from 0 to 1 =20181027
(1)给定n,证明存在唯一的x0<x1<……<xn,使得任意k均有
integrate f(x) from x(k) to x(k+1) = 2019/n
(2)证明对x0……xn,n->+∞,
证明[sigma f(x(k))]/n的极限存在并求值
任意自然数m,f(x)^(m+1)的级数展式中x^m项系数为1,求f(x)
(1)用b(1),b(2)……表示出Bell多项式系数B(7,n)(b)(n从1到7)
(2)若b(k)=1/k;任意整数m,求证
sigma B(m,n)(b)/n! =1 (n from 1 to m)
f(x)在[0,1]上连续且恒正,
integrate f(x) from 0 to 1 = 2019
integrate f(x)^2 from 0 to 1 =20181027
(1)给定n,证明存在唯一的x0<x1<……<xn,使得任意k均有
integrate f(x) from x(k) to x(k+1) = 2019/n
(2)证明对x0……xn,n->+∞,
证明[sigma f(x(k))]/n的极限存在并求值
任意自然数m,f(x)^(m+1)的级数展式中x^m项系数为1,求f(x)