DLMF:11.6.E5 (Q3981)

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DLMF:11.6.E5
No description defined

    Statements

    Defining formula
    𝐇 ν ⁡ ( z ) , 𝐋 ν ⁡ ( z ) ∼ z π ⁢ ν ⁢ 2 ⁢ ( e ⁢ z 2 ⁢ ν ) ν , asymptotically-equals Struve-H 𝜈 𝑧 modified-Struve-L 𝜈 𝑧 𝑧 𝜋 𝜈 2 superscript 𝑒 𝑧 2 𝜈 𝜈 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right),\mathbf{L}_{\nu}% \left(z\right)\sim\frac{z}{\pi\nu\sqrt{2}}\left(\frac{ez}{2\nu}\right)^{\nu},}}
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    DLMF id
    DLMF:11.6.E5
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    constraint
    | ph ⁡ ν | ≤ π - δ phase 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
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    Symbols used
    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
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    modified Struve function
    Defining formula
    𝐋 ν ⁡ ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E2.m2adec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1addec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1ddec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1bdec
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    Q11498
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1ddec
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