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. »
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Basic Examples (5)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
LogisticSigmoid threads elementwise over lists and matrices:
LogisticSigmoid can be used with Interval and CenteredInterval objects:
Specific Values (4)
The value of LogisticSigmoid at 2 πI n for integer n is 1/2:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Find a value of for which the using Solve:
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:
It has no singularities or discontinuities:
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)
Function Representations (4)
LogisticSigmoid can be represented in terms of Exp:
LogisticSigmoid can be represented in terms of MeijerG:
LogisticSigmoid obeys the logistic differential equation :
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