DLMF:10.11.E4 (Q3106)

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DLMF:10.11.E4
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    test
    sin ⁡ ( ν ⁢ π ) ⁢ H ν ( 2 ) ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = e ν ⁢ π ⁢ i ⁢ sin ⁡ ( m ⁢ ν ⁢ π ) ⁢ H ν ( 1 ) ⁡ ( z ) + sin ⁡ ( ( m + 1 ) ⁢ ν ⁢ π ) ⁢ H ν ( 2 ) ⁡ ( z ) . 𝜈 𝜋 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 𝑒 𝜈 𝜋 𝑖 𝑚 𝜈 𝜋 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 𝑚 1 𝜈 𝜋 Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle\sin\left(\nu\pi\right){H^{(2)}_{\nu}}\left(ze^{m% \pi i}\right)=e^{\nu\pi i}\sin\left(m\nu\pi\right){H^{(1)}_{\nu}}\left(z\right% )+\sin\left((m+1)\nu\pi\right){H^{(2)}_{\nu}}\left(z\right).}}
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    DLMF:10.11.E4
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