- 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.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
The expansion of the function:
Numerical Evaluation (5)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number input:
Evaluate efficiently at high precision:
LogisticSigmoid threads elementwise over lists and matrices:
Specific Values (4)
The value of LogisticSigmoid at 2 πI n for integer n is 1/2:
Values at infinity:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Find a value of for which the using Solve:
Substitute in the result:
Visualize the result:
Plot the LogisticSigmoid[x] function:
Plot the real part of :
Plot the imaginary part of :
Polar plot with :
First derivative with respect to z:
Higher derivatives with respect to z:
Plot the higher derivatives with respect to z:
Formula for the derivative with respect to z:
Compute the indefinite integral using Integrate:
Verify the anti-derivative:
Series Expansions (3)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Find the series expansion at Infinity:
Taylor expansion at a generic point:
Function Representations (4)
Introduced in 2014