Hankel H (1)

The Hankel functions of the first kind are defined by $$H_{\nu}^{(1)}(z)=J_{\nu}(z)+iY_{\nu}(z),$$ where $J_{\nu}$ is the Bessel function of the first kind and $Y_{\nu}$ is the Bessel function of the second kind. Note the similarity of these functions to the Hankel functions of the second kind.

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  Domain coloring of analytic continuation.