Bernstein polynomial and Bernstein function

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Bernstein functions and Bernstein polynomials are distinct mathematical concepts, though they share the name "Bernstein." Bernstein polynomials are used in approximation theory and are defined as a linear combination of basis functions, while Bernstein functions are non-negative, infinitely differentiable functions that are related to the theory of stochastic processes. The primary connection lies in their applications in probability and approximation, but they serve different purposes and have different properties. Further exploration of their definitions and applications can be found in the provided links. Understanding their unique characteristics is essential for grasping their roles in mathematical analysis.
Tatianaoo
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Hi! Does anybody know if there is something in common between Bernstein functions and Bernstein polynomials except the word 'Bernstein'? I mean from mathematical point of view.
 
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