DLMF:10.24.E8 (Q3486): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic cotangent function / qualifier
 
test:

coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}

\coth@@{\NVar{z}}
Property / Symbols used: hyperbolic cotangent function / qualifier
 
xml-id: C4.S28.E7.m2adec

Revision as of 12:34, 2 January 2020

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DLMF:10.24.E8
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    Statements

    test
    Y ~ ν ⁡ ( x ) = ( 2 ⁢ coth ⁡ ( 1 2 ⁢ π ⁢ ν ) π ⁢ ν ) 1 2 ⁢ sin ⁡ ( ν ⁢ ln ⁡ ( 1 2 ⁢ x ) - γ ν ) + O ⁡ ( x 2 ) , Bessel-Y-Weber-imaginary-order 𝜈 𝑥 superscript 2 hyperbolic-cotangent 1 2 𝜈 𝜈 1 2 𝜈 1 2 𝑥 subscript 𝛾 𝜈 Big-O superscript 𝑥 2 {\displaystyle{\displaystyle\widetilde{Y}_{\nu}\left(x\right)=\left(\frac{2% \coth\left(\frac{1}{2}\pi\nu\right)}{\pi\nu}\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:10.24.E8
    0 references
    constraint
    ν > 0 𝜈 0 {\displaystyle{\displaystyle\nu>0}}
    0 references
    Symbols used
    Q11479
    test
    Y ~ ν ⁡ ( x ) Bessel-Y-Weber-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{Y}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S24.Ex2.m2addec
    0 references
    order not exceeding
    test
    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
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    hyperbolic cotangent function
    test
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
     
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