Series Expansion for a Sigmoid Equation

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SUMMARY

The discussion centers on deriving a series expansion for the sigmoid equation defined as base + max/(1+exp(H-x/rate)), where base, max, H, and rate are coefficients. Participants express curiosity about the feasibility of this derivation, particularly through the application of Taylor series expansion. A suggestion is made to utilize WolframAlpha's symbolic calculator for assistance in obtaining the series expansion. The conversation indicates that while the derivation may be complex, it is not entirely unfeasible.

PREREQUISITES
  • Understanding of sigmoid functions and their properties
  • Familiarity with Taylor series expansion techniques
  • Basic knowledge of calculus, particularly limits and derivatives
  • Experience with symbolic computation tools like WolframAlpha
NEXT STEPS
  • Research the application of Taylor series expansion to non-linear functions
  • Explore the capabilities of WolframAlpha for symbolic mathematics
  • Study the mathematical properties of sigmoid functions in depth
  • Learn about alternative series expansions, such as Maclaurin series
USEFUL FOR

Mathematicians, data scientists, and anyone interested in advanced calculus applications, particularly in modeling with sigmoid functions.

hak185
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I am just curious to know if it is possible to derive a series expansion for the following sigmoid equation:

base + max/(1+exp(H-x/rate))

where the coefficients are base, max, H, and rate.

Would appreciate any insight.
 
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Seem like I can infer from the ratio of responses to views that this is not a very feasible concept...? In any case, I would appreciate any type of feedback. I would just like to get an idea of how attainable the derivation is, especially from someone who is knowledgeable on applying taylor series expansion to functions.
 
hak185 said:
I am just curious to know if it is possible to derive a series expansion for the following sigmoid equation:

base + max/(1+exp(H-x/rate))

where the coefficients are base, max, H, and rate.

Would appreciate any insight.

What type of series are you interested in? Taylor?
You can use wolframalpha's symbolic calculator: http://www.wolframalpha.com/input/?i=series+b+++m/(1+exp(H-x/r))
 

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