[分析] 我看不懂題目的意思...

[bineapple (パイナップル)]

Let f be continuous on [0,a]. If x belongs to [0,a], define f_0(x)=f(x) and
                  x     n
let f_(n+1)(x) = ∫(x-t) f(t)dt, n = 0, 1, 2,...
                  0
a) Show that the n-th derivative of f_n exists and equals f.

b) Prove the following theorem of M. Fekete: The number of changes in sign

   of f in [0,a] is not less than the number of changes in sign in the

   ordered set of numbers f(a),f_1(a),...,f_n(a).

Hint: 數學歸納法

a很簡單我會做,可是b我有點不明白題目的意思,

想請問那個n是從哪裡來的啊?

謝謝~~

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