DLMF:10.22.E60 (Q3434)

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Language	Label	Description	Also known as
English	DLMF:10.22.E60	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{ibt}Y_{0}\left(at\right)% \mathrm{d}t=\begin{cases}(2i/\pi)(a^{2}-b^{2})^{-\frac{1}{2}}\operatorname{% arcsin}\left(b/a\right),&0\leq b<a,\\ (b^{2}-a^{2})^{-\frac{1}{2}}\left(-1+\dfrac{2i}{\pi}\ln\left(\dfrac{a}{b+(b^{2% }-a^{2})^{\frac{1}{2}}}\right)\right),&0<a<b.\end{cases}}}

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DLMF:10.22.E60

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2aidec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2awdec

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Defining formula

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

C1.S4.SS4.m1abgdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abgdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

C4.S23.SS2.p1.m5aadec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2abdec

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Sitelinks

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