- Mathematical function, suitable for both symbolic and numerical manipulation.
- The inverse Gudermannian function is defined by .
- InverseGudermannian[z] has branch cut discontinuities in the complex plane running from to for integers .
- InverseGudermannian can be evaluated to arbitrary numerical precision.
- InverseGudermannian automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Asymptotic expansion at a singular point:
Numerical Evaluation (5)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
InverseGudermannian threads elementwise over lists and matrices:
Specific Values (4)
The value at zero:
Values at infinity:
Find a value of x for which the InverseGudermannian[x]=0.8 using Solve:
The first derivative with respect to x:
Higher derivatives with respect to x:
Plot the higher derivatives with respect to x:
Compute the indefinite integral using Integrate:
The definite integral:
The definite integral of InverseGudermannian over a period is 0:
Mercator projection map of the world:
Properties & Relations (2)