DLMF:6.7.E15 (Q2268): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
Defining formula:

K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2adec

Revision as of 01:29, 2 January 2020

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DLMF:6.7.E15
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    Statements

    Defining formula
    f ⁡ ( z ) = 2 ⁢ ∫ 0 ∞ K 0 ⁡ ( 2 ⁢ z ⁢ t ) ⁢ cos ⁡ t ⁢ d t , sine-cosine-integral-f 𝑧 2 superscript subscript 0 modified-Bessel-second-kind 0 2 𝑧 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=2\int_{0}^{\infty}K_{0}% \left(2\sqrt{zt}\right)\cos t\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.7.E15
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
    0 references
     
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