DLMF:10.45.E7 (Q3664)

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DLMF:10.45.E7
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    Statements

    Defining formula
    K ~ ν ⁡ ( x ) = - ( π ν ⁢ sinh ⁡ ( π ⁢ ν ) ) 1 2 ⁢ sin ⁡ ( ν ⁢ ln ⁡ ( 1 2 ⁢ x ) - γ ν ) + O ⁡ ( x 2 ) , modified-Bessel-second-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{K}_{\nu}\left(x\right)=-\left(\frac{\pi% }{\nu\sinh\left(\pi\nu\right)}\right)^{\frac{1}{2}}\*\sin\left(\nu\ln\left(% \tfrac{1}{2}x\right)-\gamma_{\nu}\right)+O\left(x^{2}\right),}}
    0 references
    DLMF id
    DLMF:10.45.E7
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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