DLMF:10.39.E10 (Q3578)

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DLMF:10.39.E10
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    Statements

    Defining formula
    I ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν ⁢ lim ⁡ 𝐅 ⁡ ( λ , μ ; ν + 1 ; z 2 / ( 4 ⁢ λ ⁢ μ ) ) , modified-Bessel-first-kind 𝜈 𝑧 superscript 1 2 𝑧 𝜈 scaled-hypergeometric-bold-F 𝜆 𝜇 𝜈 1 superscript 𝑧 2 4 𝜆 𝜇 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{\nu}\lim% \mathbf{F}\left(\lambda,\mu;\nu+1;z^{2}/(4\lambda\mu)\right),}}
    0 references
    DLMF id
    DLMF:10.39.E10
    0 references
    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.m2addec
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    $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
    Defining formula
    𝐅 ⁡ ( a , b ; c ; z ) scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}
    xml-id
    C15.S2.E2.m2adec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1idec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1edec
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