Kelvin bei

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The $\mathrm{bei}_{\nu}$ function is defined as $$\mathrm{ber}(z)=\mathrm{Im} \hspace{2pt} J_{\nu} \left( x e^{\frac{3\pi i}{4}} \right),$$ where $\mathrm{Ie}$ denotes the imaginary part of a complex number and $J_{\nu}$ denotes the Bessel function of the first kind.