This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


gives the Gudermannian function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Gudermannian function is defined by .
  • Gudermannian[z] has branch cut discontinuities in the complex plane running from to for integers .
  • Gudermannian can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
Exact evaluation:
Gudermannian threads element-wise over lists:
TraditionalForm formatting:
Gudermannian can be applied to a power series:
Non-periodic solution of a pendulum equation:
Use FunctionExpand to expand Gudermannian in terms of elementary functions:
Use FullSimplify to prove identities involving the Gudermannian function:
New in 7