Tanc function: Difference between revisions

Revision as of 12:00, 17 March 2015

Revision as of 12:02, 17 March 2015

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In mathematics, the '''Tanc function''' is defined as<ref>Weisstein, Eric W. "Tanc Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TancFunction.html </ref>

: <math>\operatorname{Tanc}(z)=\frac {\tanhtan(z) }{z}</math>

[[File:Tanc 2D plot.png|thumb|Tanc 2D plot]]

[[File:Tanc'(z) 2D plot.png|thumb|Tanc'(z) 2D plot]]

[[File:Tanc integral 2D plot.png|thumb|Tanc integral 2D plot]]

;Imaginary part in complex plane

*<math> \operatorname{Im} \left( \frac {\tanhtan(x+iy) }{x+iy} \right) </math>

;Real part in complex plane

*<math> \operatorname{Re} \left( \frac {\tanhtan \left( x+iy \right) }{x+iy} \right) </math>

;absolute magnitude

*<math> \left| \frac {\tanhtan(x+iy) }{x+iy} \right| </math>

;First-order derivative

*<math> \frac {1- \tanhtan(z))^2}{z} - \frac {\tanhtan(z)}{z^2} </math>

;Real part of derivative

*<math> -\operatorname{Re} \left( -\frac {1- (\tanhtan(x+iy))^2}{x+iy} +\frac{\tanhtan(x+iy)}{(x+iy)^2} \right)

</math>

;Imaginary part of derivative

*<math>-\operatorname{Im} \left( -\frac {1-(\tanhtan(x+iy))^2}{x+iy} + \frac {\tanhtan(x+iy)}{(x+iy)^2} \right)

</math>

;absolute value of derivative

*<math> \left| -\frac{1-(\tanhtan(x+iy))^2}{x+iy}+\frac {\tanhtan(x+iy)}{(x+iy)^2} \right| </math>

==In terms of other special functions==

Line 35 ⟶ 38:

==Gallery==

{|

|[[File:Tanc abs complex 3D plot.png|thumb|Tanc abs complex 3D]]

|[[File:Tanc Im complex 3D plot.png|thumb|Tanc Im complex 3D plot]]

|[[File:Tanc Re complex 3D plot.png|thumb|Tanc Re complex 3D plot]]

|}

{|

|[[File:Tanc'(z) Im complex 3D plot.png|thumb|Tanc'(z) Im complex 3D plot]]

|[[File:Tanc'(z) Re complex 3D plot.png|thumb|Tanc'(z) Re complex 3D plot]]

|[[File:Tanc'(z) abs complex 3D plot.png|thumb|Tanc'(z) abs complex 3D plot]]

|

|}

{|

|[[File:Tanc abs plot.JPG|thumb|Tanc abs plot]]

|[[File:Tanc Im plot.JPG|thumb|Tanc Im plot]]

|[[File:Tanc Re plot.JPG|thumb|Tanc Re plot]]

|}

{|

|[[File:Tanc'(z) Im plot.JPG|thumb|Tanc'(z) Im plot]]

|[[File:Tanc'(z) abs plot.JPG|thumb|Tanc'(z) abs plot]]

|[[File:Tanc'(z) Re plot.JPG|thumb|Tanc'(z) Re plot]]

|}