DLMF:10.54#Ex2 (Q3764)

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DLMF:10.54#Ex2
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    Statements

    Defining formula
    𝗁 n ( 2 ) ⁡ ( z ) = ( - i ) n + 1 π ⁢ ∫ i ⁢ ∞ ( - 1 + ) e i ⁢ z ⁢ t ⁢ Q n ⁡ ( t ) ⁢ d t , spherical-Hankel-H-2-Bessel-third-kind 𝑛 𝑧 superscript 𝑖 𝑛 1 𝜋 superscript subscript 𝑖 limit-from 1 superscript 𝑒 𝑖 𝑧 𝑡 shorthand-Legendre-Q-second-kind 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{n}}\left(z\right)=\frac{(-i)^{n% +1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}Q_{n}\left(t\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:10.54#Ex2
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π . phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi.}}
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