Difference between revisions of "Kelvin ber"
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The $\mathrm{ber}_{\nu}$ function is defined as | The $\mathrm{ber}_{\nu}$ function is defined as | ||
| − | $$\mathrm{ber}(z)=\mathrm{Re} \hspace{2pt} J_{\nu} \left( | + | $$\mathrm{ber}_{\nu}(z)=\mathrm{Re} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$ |
| − | where $\mathrm{Re}$ denotes the [[real part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J | + | where $\mathrm{Re}$ denotes the [[real part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]]. |
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Kelvinber,n=0plot.png|Graph of $\mathrm{ber}_0$. | ||
| + | File:Kelvinber,n=0.5plot.png|Graph of $\mathrm{ber}_{\frac{1}{2}}$. | ||
| + | File:Kelvinber,n=1plot.png|Graph of $\mathrm{ber}_1$. | ||
| + | File:Kelvinber,n=2plot.png|Graph of $\mathrm{ber}_2$. | ||
| + | File:Complexkelvinber,n=0plot.png|[[Domain coloring]] of $\mathrm{ber}_0$. | ||
| + | File:Complexkelvinber,n=1plot.png|[[Domain coloring]] of $\mathrm{ber}_1$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Higher Transcendental Functions Volume II|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=findme|next=Kelvin bei}}: $\S 7.2.3 (19)$ | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
| + | |||
| + | {{:Kelvin functions footer}} | ||
Latest revision as of 05:41, 4 March 2018
The $\mathrm{ber}_{\nu}$ function is defined as $$\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.
Graph of $\mathrm{ber}_0$.
Graph of $\mathrm{ber}_{\frac{1}{2}}$.
Graph of $\mathrm{ber}_1$.
Graph of $\mathrm{ber}_2$.
Domain coloring of $\mathrm{ber}_0$.
Domain coloring of $\mathrm{ber}_1$.
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume II ... (previous) ... (next): $\S 7.2.3 (19)$
