DLMF:10.11.E7 (Q3110)

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DLMF:10.11.E7
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    H n ( 1 ) ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = ( - 1 ) m ⁢ n - 1 ⁢ ( ( m - 1 ) ⁢ H n ( 1 ) ⁡ ( z ) + m ⁢ H n ( 2 ) ⁡ ( z ) ) , Hankel-H-1-Bessel-third-kind 𝑛 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 1 𝑚 𝑛 1 𝑚 1 Hankel-H-1-Bessel-third-kind 𝑛 𝑧 𝑚 Hankel-H-2-Bessel-third-kind 𝑛 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{n}}\left(ze^{m\pi i}\right)=(-1)^{mn-1}(% (m-1){H^{(1)}_{n}}\left(z\right)+m{H^{(2)}_{n}}\left(z\right)),}}
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    DLMF:10.11.E7
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