Is there a general formula for I n = ∫ 0 1 ( x −...

vasorasy8

vasorasy8

Answered

2022-07-10

Is there a general formula for
I n = 0 1 ( x 1 ) ( x 2 ) ( x n ) d x

Answer & Explanation

behk0

behk0

Expert

2022-07-11Added 14 answers

In terms of the Stirling numbers of the first kind,
( x 1 ) ( x 2 ) ( x n ) = k = 0 n s ( n , k ) ( x 1 ) k .
Thus,
I n = k = 0 n ( 1 ) k s ( n , k ) k + 1 .
Asymptotically,
I n ( 1 ) n n ! log n
as n +

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