Kelvin ber

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