gives the logistic sigmoid function.
- Mathematical function, suitable for both symbolic and numeric manipulation.
- In TraditionalForm, the logistic sigmoid function is sometimes denoted as .
- The logistic function is a solution to the differential equation .
- LogisticSigmoid[z] has no branch cut discontinuities.
- LogisticSigmoid can be evaluated to arbitrary numerical precision.
- LogisticSigmoid automatically threads over lists.
- LogisticSigmoid can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (5)
Numerical Evaluation (6)
LogisticSigmoid threads elementwise over lists and matrices:
Specific Values (4)
Plot the LogisticSigmoid[x] function:
Function Properties (10)
LogisticSigmoid is defined for all real and complex values:
LogisticSigmoid achieves all values between 0 and 1 on the reals:
LogisticSigmoid has the mirror property :
LogisticSigmoid is an analytic function of x:
LogisticSigmoid is nondecreasing:
LogisticSigmoid is injective:
LogisticSigmoid is not surjective:
LogisticSigmoid is non-negative:
LogisticSigmoid is neither convex nor concave:
Compute the indefinite integral using Integrate:
Series Expansions (3)
The following differential equation is solved with LogisticSigmoid:
Wolfram Research (2014), LogisticSigmoid, Wolfram Language function, https://reference.wolfram.com/language/ref/LogisticSigmoid.html.
Wolfram Language. 2014. "LogisticSigmoid." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LogisticSigmoid.html.
Wolfram Language. (2014). LogisticSigmoid. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogisticSigmoid.html