An Inequalities for the Integral with a Parameter

Xie Yongdong

Xie Yongdong. An Inequalities for the Integral with a Parameter[J]. Journal of nanchang hangkong university(Natural science edition), 1998, 12(1): 12-16.

Citation:

Xie Yongdong. An Inequalities for the Integral with a Parameter[J]. Journal of nanchang hangkong university(Natural science edition), 1998, 12(1): 12-16.

Citation:

Xie Yongdong. An Inequalities for the Integral with a Parameter[J]. Journal of nanchang hangkong university(Natural science edition), 1998, 12(1): 12-16.

An Inequalities for the Integral with a Parameter

Xie Yongdong

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let p≠1 be a positive number.As to exponential integral ∫₀^xe^{-t^p}dt,We determine all numbers α=α(p)andβ=β(p)such that the inequalities1-e^{-βx^p}^1/p<1/Γ(1+1/p)∫₀^xe^{-t^p}dt<1-e^{-αx^p}^1/p(x>0)are valid for all x>0.

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