DLMF:11.9.E9 (Q4017)

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DLMF:11.9.E9
No description defined

    Statements

    Defining formula
    S μ , ν ⁡ ( z ) ∼ z μ - 1 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ a k ⁢ ( - μ , ν ) ⁢ z - 2 ⁢ k , asymptotic-expansion Lommel-S 𝜇 𝜈 𝑧 superscript 𝑧 𝜇 1 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑎 𝑘 𝜇 𝜈 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)\sim z^{\mu-1}\sum_{% k=0}^{\infty}(-1)^{k}a_{k}(-\mu,\nu)z^{-2k},}}
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    DLMF id
    DLMF:11.9.E9
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    constraint
    | ph ⁡ z | ≤ π - δ ( < π ) phase 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
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    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
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    | ph ⁡ z | ≤ π - δ ( < π ) ph 𝑧 annotated 𝜋 𝛿 absent 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
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    Symbols used
    Lommel function
    Defining formula
    S μ , ν ⁡ ( z ) Lommel-S 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle S_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}
    xml-id
    C11.S9.E5.m2abdec
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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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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.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1gdec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1hdec
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    Q11497
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1ddec
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    Q11498
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1dec
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    Q11505
    Defining formula
    a k ⁢ ( μ , ν ) subscript 𝑎 𝑘 𝜇 𝜈 {\displaystyle{\displaystyle a_{k}(\mu,\nu)}}
    xml-id
    C11.S9.XMD4.m1dec
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