DLMF:10.22.E44 (Q3418): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E44	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu}Y_{\nu}\left(t\right)% \mathrm{d}t=\frac{2^{\mu}}{\pi}\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+% \tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}% \right)\sin\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu\right)\pi,}}

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DLMF:10.22.E44

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{\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}

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{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}

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Bessel function of the second kind

Defining formula

{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E3.m2aedec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2ajdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aqdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aaqdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aaqdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aydec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2amdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1addec

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