DLMF:2.6.E5 (Q830): Difference between revisions

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Property / constraint
 

s = 0 , 1 , 2 , 𝑠 0 1 2 {\displaystyle{\displaystyle s=0,1,2,\dots}}

s=0,1,2,\dots
Property / constraint: s = 0 , 1 , 2 , 𝑠 0 1 2 {\displaystyle{\displaystyle s=0,1,2,\dots}} / rank
 
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Revision as of 16:53, 30 December 2019

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DLMF:2.6.E5
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    Statements

    0 t - s - ( 1 / 3 ) x + t d t = 2 π 3 ( - 1 ) s x s + ( 1 / 3 ) , superscript subscript 0 superscript 𝑡 𝑠 1 3 𝑥 𝑡 𝑡 2 𝜋 3 superscript 1 𝑠 superscript 𝑥 𝑠 1 3 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{-s-(1/3)}}{x+t}\mathrm{d% }t=\frac{2\pi}{\sqrt{3}}\frac{(-1)^{s}}{x^{s+(1/3)}},}}
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    s = 0 , 1 , 2 , 𝑠 0 1 2 {\displaystyle{\displaystyle s=0,1,2,\dots}}
    0 references