DLMF:10.45.E6 (Q3663)

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Language	Label	Description	Also known as
English	DLMF:10.45.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\widetilde{I}_{\nu}\left(x\right)=\left(\frac{% \sinh\left(\pi\nu\right)}{\pi\nu}\right)^{\frac{1}{2}}\cos\left(\nu\ln\left(% \tfrac{1}{2}x\right)-\gamma_{\nu}\right)+O\left(x^{2}\right),}}

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DLMF:10.45.E6

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

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modified Bessel function of the first kind of imaginary order

Defining formula

{\displaystyle{\displaystyle\widetilde{I}_{\NVar{\nu}}\left(\NVar{x}\right)}}

C10.S45.E2.m2addec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1edec

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Defining formula

{\displaystyle{\displaystyle\gamma_{\nu}}}

C10.S24.XMD1.m1dec

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Sitelinks

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