DLMF:11.6.E7 (Q4680)

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DLMF:11.6.E7
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    Statements

    DLMF defining formula
    𝐌 ν ⁡ ( λ ⁢ ν ) ∼ - ( 1 2 ⁢ λ ⁢ ν ) ν - 1 π ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ ∑ k = 0 ∞ k ! ⁢ c k ⁢ ( i ⁢ λ ) ν k , asymptotic-expansion associated-Struve-M 𝜈 𝜆 𝜈 superscript 1 2 𝜆 𝜈 𝜈 1 𝜋 Euler-Gamma 𝜈 1 2 superscript subscript 𝑘 0 𝑘 subscript 𝑐 𝑘 𝑖 𝜆 superscript 𝜈 𝑘 {\displaystyle{\displaystyle\mathbf{M}_{\nu}\left(\lambda\nu\right)\sim-\frac{% (\frac{1}{2}\lambda\nu)^{\nu-1}}{\sqrt{\pi}\Gamma\left(\nu+\frac{1}{2}\right)}% \sum_{k=0}^{\infty}\frac{k!c_{k}(i\lambda)}{\nu^{k}},}}
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    constraint
    | ph ⁡ ν | ≤ 1 2 ⁢ π - δ phase 𝜈 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\frac{1}{2}\pi-\delta}}
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    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    modified Struve function
    DLMF defining formula
    𝐌 ν ⁡ ( z ) associated-Struve-M 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E6.m2abdec
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    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1afdec
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    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ddec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1edec
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    arbitrary small positive constant
    DLMF defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1fdec
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    parameter
    DLMF defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S6.XMD1.m1adec
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    expansion function
    DLMF defining formula
    c k ⁢ ( λ ) subscript 𝑐 𝑘 𝜆 {\displaystyle{\displaystyle c_{k}(\lambda)}}
    xml-id
    C11.S6.XMD2.m1adec
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    Identifiers

     
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