DLMF:10.39.E7 (Q3575)

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DLMF:10.39.E7
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    Statements

    test
    I ν ⁡ ( z ) = ( 2 ⁢ z ) - 1 2 ⁢ M 0 , ν ⁡ ( 2 ⁢ z ) 2 2 ⁢ ν ⁢ Γ ⁡ ( ν + 1 ) , modified-Bessel-first-kind 𝜈 𝑧 superscript 2 𝑧 1 2 Whittaker-confluent-hypergeometric-M 0 𝜈 2 𝑧 superscript 2 2 𝜈 Euler-Gamma 𝜈 1 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(2z)^{-\frac{1}{2}}M_% {0,\nu}\left(2z\right)}{2^{2\nu}\Gamma\left(\nu+1\right)},}}
    0 references
    DLMF id
    DLMF:10.39.E7
    0 references
    constraint
    2 ⁢ ν ≠ - 1 , - 2 , - 3 , … 2 𝜈 1 2 3 … {\displaystyle{\displaystyle 2\nu\neq-1,-2,-3,\dots}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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