gives the Gudermannian function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Gudermannian function is generically defined by .
- Gudermannian[z] has branch cut discontinuities in the complex plane running from to for integers , where the function is continuous from the right.
- Gudermannian can be evaluated to arbitrary numerical precision.
- Gudermannian automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
Numerical Evaluation (5)
Exp threads elementwise over lists and matrices:
Specific Values (3)
Find a value of for which the using Solve:
Function Properties (11)
Gudermannian is defined for all real values:
Gudermannian is defined for all complex values except branch points:
Gudermannian has the mirror property :
Gudermannian is an odd function:
Gudermannian is non-decreasing:
Gudermannian is injective:
Gudermannian is neither non-negative nor non-positive:
Gudermannian has no singularities or discontinuities:
Gudermannian is neither convex nor concave:
Series Expansions (4)
Function Representations (4)
Since Gudermannian is odd, the same result is obtained for negative :
Represent Gudermannian using Piecewise:
Wolfram Research (2008), Gudermannian, Wolfram Language function, https://reference.wolfram.com/language/ref/Gudermannian.html (updated 2020).
Wolfram Language. 2008. "Gudermannian." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/Gudermannian.html.
Wolfram Language. (2008). Gudermannian. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Gudermannian.html