DLMF:9.12.E23 (Q2951): Difference between revisions

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imported>Admin
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imported>Admin
Property / constraint
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x > 0 π‘₯ 0 {\displaystyle{\displaystyle x>0}}

x>0
Property / constraint: x > 0 π‘₯ 0 {\displaystyle{\displaystyle x>0}} / rank
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Normal rank

Revision as of 16:14, 30 December 2019

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DLMF:9.12.E23
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    Statements

    Gi ⁑ ( x ) = 4 ⁒ x 2 3 3 / 2 ⁒ Ο€ 2 ⁒ ⨍ 0 ∞ K 1 / 3 ⁑ ( t ) ΞΆ 2 - t 2 ⁒ d t , Scorer-Gi π‘₯ 4 superscript π‘₯ 2 superscript 3 3 2 superscript πœ‹ 2 superscript subscript principal-value-integral 0 modified-Bessel-second-kind 1 3 𝑑 superscript 𝜁 2 superscript 𝑑 2 𝑑 {\displaystyle{\displaystyle\mathrm{Gi}\left(x\right)=\frac{4x^{2}}{3^{3/2}\pi% ^{2}}\pvint_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}-t^{2}}\mathrm{d% }t,}}
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    x > 0 π‘₯ 0 {\displaystyle{\displaystyle x>0}}
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