What does H represent in the graph of y = 2H(x - 4)?

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In the discussion, "H" in the equation y = 2H(x - 4) is interpreted as the Heaviside step function, which has varying definitions regarding its value at zero. The Heaviside function is defined as 0 for x < 0, 1/2 for x = 0, and 1 for x > 0, with some sources suggesting the standard definition is H(0) = 1/2. The choice of definition may depend on the context, particularly in applications like Fourier series where H(0) = 1/2 can help address the Gibbs phenomenon. The discussion emphasizes that the specific definition of H(0) may not significantly impact particle applications. Understanding the correct definition is crucial for accurately sketching the graph of the function.
jaja1990
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What does "H" mean?!

I have this question in my assignment paper:-

8. Sketch the graph of:
(a)
y = |2x − 2|;
(b)
y = 2H(x − 4)

(a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?
 
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The webpage in the link you've given says:-
The function is:-
0 when x < 0,
1/2 when x = 0,
1 when x > 0.
But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:-
1 when x => 0,
0 when x < 0.

To begin with, which should I follow?
 


I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in particle applications.
 


JJacquelin said:
I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in particle applications.

If one wanted to use an approximation like a Fourier series version, then it makes sense to define H(0) as 1/2 based on properties of Fourier series when you have this kind of 'Gibbs' phenomenon.
 
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