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\right) {{\rm KummerM}\left(1,\,2,\,i \left( 2\,z+\pi \right) \right)}}}</math>
*<math>\operatorname{Tanc}(z)={ \frac {22i \operatorname{HeunB} \left( 2,i0,0,0,\sqrt {2}\itsqrt {iz} \right) }{(2z+\pi) \operatorname{HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {iz(i/2) (2z+\pi) } \right) }{ </math>
\left( 2\,z+\pi \right) {\it HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {1
/2\,i \left( 2\,z+\pi \right) } \right) }} </math>
* <math>\operatorname{Tanc}(z)={ \frac {{{\rm WhittakerM}\left(0,\,1/2,\,2\,iz\right)}}{{\rm WhittakerM}(0,\,1/2,\,i (2z+\pi)) z}
{{\rm WhittakerM}\left(0,\,1/2,\,i \left( 2\,z+\pi \right) \right)}z}}
</math>
==Series expansion==
: <math>\operatorname{Tanc} z \approx \left(1+{ \frac {1}{3}}{ z}^{2} +{ \frac {2}{15}}{ z}^{4} +{ \frac {17}{315}}{ z}^{6} +{ \frac {62}{2835}}{ z}^{8} +{ \frac {1382}{155925}}{ z}^{10} + \frac{21844}{6081075} z^{12}+ \frac {929569}{638512875} z^{14} + O(z^{16} ) \right)</math>
21844}{6081075}}{z}^{12}+{\frac {929569}{638512875}}{z}^{14}+O \left(
: <math>\int _0^z \frac {\tan(x) }{x} \, dx = \left(z+ \frac {1}{9} z^3 + \frac {2}{75} z^5 + \frac {17}{2205} z^7 + \frac {62}{25515} z^9+ \frac {1382}{1715175} z^{11}+ \frac {21844}{
{z}^{16} \right) )</math>
79053975} }{ z }^{13} + { \frac {929569}{9577693125} }{ z }^{15}+ O \left( {z }^{ 17}) \right)</math>▼:<math>\int _{0}^{z}\!{\frac {\tan \left( x \right) }{x}}{dx}=(z+{\frac {1}{9
}}{z}^{3}+{\frac {2}{75}}{z}^{5}+{\frac {17}{2205}}{z}^{7}+{\frac {62}
{25515}}{z}^{9}+{\frac {1382}{1715175}}{z}^{11}+{\frac {21844}{
▲79053975}}{z}^{13}+{\frac {929569}{9577693125}}{z}^{15}+O \left( {z}^{
17} \right) )</math>
==Gallery==
|[[File:Tanc Re complex 3D plot2.JPG|thumb|Tanc Re complex 3D plot]]
|}
==See also==
* [[TanhcSinhc function]]
* [[CoshcTanhc function]]
▲* [[ SinhcCoshc function]]
==References==
| 