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DLMF:10.40.E6 - MaRDI portal

DLMF:10.40.E6 (Q4281)

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DLMF:10.40.E6
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    Statements

    DLMF defining formula
    I ν ⁡ ( z ) ⁢ K ν ⁡ ( z ) ∼ 1 2 ⁢ z ⁢ ( 1 - 1 2 ⁢ μ - 1 ( 2 ⁢ z ) 2 + 1 ⋅ 3 2 ⋅ 4 ⁢ ( μ - 1 ) ⁢ ( μ - 9 ) ( 2 ⁢ z ) 4 - ⋯ ) , asymptotic-expansion modified-Bessel-first-kind 𝜈 𝑧 modified-Bessel-second-kind 𝜈 𝑧 1 2 𝑧 1 1 2 𝜇 1 superscript 2 𝑧 2 ⋅ 1 3 ⋅ 2 4 𝜇 1 𝜇 9 superscript 2 𝑧 4 ⋯ {\displaystyle{\displaystyle I_{\nu}\left(z\right)K_{\nu}\left(z\right)\sim% \frac{1}{2z}\left(1-\frac{1}{2}\frac{\mu-1}{(2z)^{2}}+\frac{1\cdot 3}{2\cdot 4% }\frac{(\mu-1)(\mu-9)}{(2z)^{4}}-\cdots\right),}}
    0 references
    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
    0 references
    modified Bessel function of the first kind
    DLMF defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2acdec
    0 references
    modified Bessel function of the second kind
    DLMF 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.m2abdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1edec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1edec
    0 references

    Identifiers

     
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