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

Error creating thumbnail: Unable to save thumbnail to destination

Graph of $\mathrm{ber}_0$.
Error creating thumbnail: Unable to save thumbnail to destination

Graph of $\mathrm{ber}_{\frac{1}{2}}$.
Error creating thumbnail: Unable to save thumbnail to destination

Graph of $\mathrm{ber}_1$.
Error creating thumbnail: Unable to save thumbnail to destination

Graph of $\mathrm{ber}_2$.
Error creating thumbnail: Unable to save thumbnail to destination

Domain coloring of $\mathrm{ber}_0$.
Error creating thumbnail: Unable to save thumbnail to destination

Domain coloring of $\mathrm{ber}_1$.

References

1953: {{ #if: |{{{2}}}|Arthur Erdélyi}}{{#if: Wilhelm Magnus|{{#if: Fritz Oberhettinger|, {{ #if: |{{{2}}}|Wilhelm Magnus}}{{#if: Francesco G. Tricomi|, {{ #if: |{{{2}}}|Fritz Oberhettinger}}{{#if: |, {{ #if: |{{{2}}}|Francesco G. Tricomi}}{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and {{ #if: |{{{2}}}|Francesco G. Tricomi}}}}| and {{ #if: |{{{2}}}|Fritz Oberhettinger}}}}| and {{ #if: |{{{2}}}|Wilhelm Magnus}}}}|}}: [[Book:Arthur Erdélyi/Higher Transcendental Functions Volume II{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|Higher Transcendental Functions Volume II{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: findme | ... (previous)|}}{{#if: Kelvin bei | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}}: $\S 7.2.3 (19)$