DLMF:11.4.E3 (Q3935)

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DLMF:11.4.E3
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    Statements

    Defining formula
    𝐇 - n - 1 2 ⁡ ( z ) = ( - 1 ) n ⁢ J n + 1 2 ⁡ ( z ) , Struve-H 𝑛 1 2 𝑧 superscript 1 𝑛 Bessel-J 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{-n-\frac{1}{2}}\left(z\right)=(-1)^{n}% J_{n+\frac{1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.4.E3
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
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    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2adec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1bdec
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