Gudermannian[z] gives the Gudermannian function gd (z).

Evaluate numerically: In[1]:=Gudermannian[4.2] Out[1]=1.54081 Plot over a subset of the reals: In[1]:=Plot[Gudermannian[x], {x, -10, 10}] Out[1]= Plot over a subset of the complexes: In[1]:=ComplexPlot3D[Gudermannian[z], {z, -2 - 2I π, 2 + 2I π}, PlotLegends->Automatic] Out[1]=

Listable | NumericFunction | Protected | ReadProtected

Christoph Gudermann

InverseGudermannian | ArcTan

1895th most common (1 in 456000 symbols)

1899th most common (1 in 3700000 symbols)

3024th most common (1 in 100000 symbols)

introduced in Version 7 (November 2008) last modified in Version 12.1 (March 2020)