DLMF:10.41.E12 (Q3609)

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DLMF:10.41.E12
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    Statements

    Defining formula
    I ν ⁡ ( ν ⁢ z ) = e ν ⁢ η ( 2 ⁢ π ⁢ ν ) 1 2 ⁢ ( 1 + z 2 ) 1 4 ⁢ ( ∑ k = 0 ℓ - 1 U k ⁢ ( p ) ν k + O ⁡ ( 1 z ℓ ) ) , modified-Bessel-first-kind 𝜈 𝜈 𝑧 superscript 𝑒 𝜈 𝜂 superscript 2 𝜋 𝜈 1 2 superscript 1 superscript 𝑧 2 1 4 superscript subscript 𝑘 0 ℓ 1 subscript 𝑈 𝑘 𝑝 superscript 𝜈 𝑘 Big-O 1 superscript 𝑧 ℓ {\displaystyle{\displaystyle I_{\nu}\left(\nu z\right)=\frac{e^{\nu\eta}}{(2% \pi\nu)^{\frac{1}{2}}(1+z^{2})^{\frac{1}{4}}}\left(\sum_{k=0}^{\ell-1}\frac{U_% {k}(p)}{\nu^{k}}+O\left(\frac{1}{z^{\ell}}\right)\right),}}
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    DLMF id
    DLMF:10.41.E12
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    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
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