DLMF:9.7.E11 (Q2818)

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DLMF:9.7.E11
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    Statements

    test
    Bi ⁡ ( - z ) ∼ 1 π ⁢ z 1 / 4 ⁢ ( - sin ⁡ ( ζ - 1 4 ⁢ π ) ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ u 2 ⁢ k ζ 2 ⁢ k + cos ⁡ ( ζ - 1 4 ⁢ π ) ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ u 2 ⁢ k + 1 ζ 2 ⁢ k + 1 ) , asymptotic-expansion Airy-Bi 𝑧 1 𝜋 superscript 𝑧 1 4 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑢 2 𝑘 superscript 𝜁 2 𝑘 𝜁 1 4 𝜋 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑢 2 𝑘 1 superscript 𝜁 2 𝑘 1 {\displaystyle{\displaystyle\mathrm{Bi}\left(-z\right)\sim\frac{1}{\sqrt{\pi}z% ^{1/4}}\left(-\sin\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{\infty}(-1)^{k% }\frac{u_{2k}}{\zeta^{2k}}+\cos\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{% \infty}(-1)^{k}\frac{u_{2k+1}}{\zeta^{2k+1}}\right),}}
    0 references
    DLMF id
    DLMF:9.7.E11
    0 references
    constraint
    | ph ⁡ z | ≤ 2 3 ⁢ π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}
    0 references
    Symbols used
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2abdec
    0 references
     
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