DLMF:10.33.E2 (Q3541)

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DLMF:10.33.E2
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    Statements

    Defining formula
    I ν ⁡ ( z ) I ν - 1 ⁡ ( z ) = 1 2 ⁢ z / ν 1 + ⁢ 1 4 ⁢ z 2 / ( ν ⁢ ( ν + 1 ) ) 1 + ⁢ 1 4 ⁢ z 2 / ( ( ν + 1 ) ⁢ ( ν + 2 ) ) 1 + ⁢ ⋯ , modified-Bessel-first-kind 𝜈 𝑧 modified-Bessel-first-kind 𝜈 1 𝑧 continued-fraction 1 2 𝑧 𝜈 limit-from 1 continued-fraction 1 4 superscript 𝑧 2 𝜈 𝜈 1 limit-from 1 continued-fraction 1 4 superscript 𝑧 2 𝜈 1 𝜈 2 limit-from 1 ⋯ {\displaystyle{\displaystyle\frac{I_{\nu}\left(z\right)}{I_{\nu-1}\left(z% \right)}=\cfrac{\frac{1}{2}z/\nu}{1+}\cfrac{\frac{1}{4}z^{2}/(\nu(\nu+1))}{1+}% \cfrac{\frac{1}{4}z^{2}/((\nu+1)(\nu+2))}{1+}\cdots,}}
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    DLMF id
    DLMF:10.33.E2
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    constraint
    ν ≠ 0 , - 1 , - 2 , … 𝜈 0 1 2 … {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}}
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    Symbols used
    modified Bessel function of the first kind
    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.m2aadec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
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