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BUILT-IN MATHEMATICA SYMBOL
Gudermannian
Tan
See Also »
|
Summary of New Features in 7.0
Trigonometric Functions
New in 7.0: Alphabetical Listing
More About »
InverseGudermannian
InverseGudermannian
[
z
]
gives the inverse Gudermannian function
.
MORE INFORMATION
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.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
In[1]:=
Out[1]=
Scope
(6)
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
Exact evaluations:
TraditionalForm
formatting:
Generalizations & Extensions
(1)
InverseGudermannian
can be applied to a power series:
Applications
(1)
Mercator projection map of the world:
Properties & Relations
(2)
Derivative of the inverse Gudermannian function:
Use
FunctionExpand
to expand
InverseGudermannian
in terms of elementary functions:
SEE ALSO
Gudermannian
Tan
MORE ABOUT
Summary of New Features in 7.0
Trigonometric Functions
New in 7.0: Alphabetical Listing
New in 7
.
.
plane running from 
to 
for integers 
.
EXAMPLES
Basic Examples 
Scope 