DLMF:10.45.E6 (Q3663)

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DLMF:10.45.E6
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    I ~ ν ( x ) = ( sinh ( π ν ) π ν ) 1 2 cos ( ν ln ( 1 2 x ) - γ ν ) + O ( x 2 ) , modified-Bessel-first-kind-imaginary-order 𝜈 𝑥 superscript 𝜋 𝜈 𝜋 𝜈 1 2 𝜈 1 2 𝑥 subscript 𝛾 𝜈 Big-O superscript 𝑥 2 {\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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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2aadec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2adec
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    I ~ ν ( x ) modified-Bessel-first-kind-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{I}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S45.E2.m2addec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
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