DLMF:10.67.E8 (Q3853)

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Language	Label	Description	Also known as
English	DLMF:10.67.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{bei}_{\nu}'x\sim\frac{e^{x/\sqrt{2}}% }{(2\pi x)^{\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{x^{k}}\sin% \left(\frac{x}{\sqrt{2}}+\left(\frac{\nu}{2}+\frac{3k}{4}+\frac{1}{8}\right)% \pi\right)+\frac{1}{\pi}(\cos\left(2\nu\pi\right)\operatorname{ker}_{\nu}'x-% \sin\left(2\nu\pi\right)\operatorname{kei}_{\nu}'x).}}

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DLMF:10.67.E8

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Kelvin function

Defining formula

{\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C10.S61.E1.m3aadec

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Kelvin function

Defining formula

{\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C10.S61.E2.m3aedec

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Kelvin function

Defining formula

{\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C10.S61.E2.m2aedec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11agdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2agdec

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Defining formula

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

C4.S14.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1gdec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1gdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1gdec

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expansion (locally)

Defining formula

{\displaystyle{\displaystyle b_{k}(\nu)}}

C10.S17.XMD3.m1cdec

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Sitelinks

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