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I have been in trouble with the hump function(s) What are them?

Could you give me an explicit formula for "Hump"(not bump) function.

Thanks

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    The mathematician's fetish equivalent of [this](http://www.reddit.com/r/AskReddit/comments/r7uor/my_friend_built_a_robot_pig_for_him_to_have_sex/)? Or more seriously: [A function used in optimisation](http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/Page1621.htm)?2012-03-22
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    Could you tell us about the context in which you came across the term "hump" function? Is it possible someone *meant* bump function but said "hump"? You could have also included the problem behind this: "find a $\mathcal{C}^\infty$ function with analyticity set $\emptyset$" ([on MO](http://mathoverflow.net/questions/91894/what-is-a-hump-function), if that is indeed you).2012-03-22
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    @anon, that is exactly the context I was asked this question.2012-03-22
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    Tolstov uses the word "hump" [here](http://books.google.si/books?id=XqqNDQeLfAkC&pg=PA84&lpg=PA84&dq=hump+function+tolstov+fourier+series&source=bl&ots=dPTgIus3Nq&sig=L_lcy0gTn4g-jZ0AxTAe8Vv82ro&hl=sl&sa=X&ei=wwtrT8-6GIOVswan9PCKAg&ved=0CBwQ6AEwAA#v=onepage&q&f=false). I thought it might be related.2012-03-22
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    Often the two names are used for the same thing.2012-03-22
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    In my neighbourhood there are speed humps. I have never understood the difference.2012-03-22
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    MATLAB has something called the `humps()` function which it uses for demonstrating quadrature, optimization, and rootfinding routines.2012-03-24
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    With either name, it would seem something climactic is happening in a short interval of time.2017-07-19

2 Answers 2

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If you're referring to the category of functions called humps that I'm familiar with, then of one these functions is $f$ defined below (try plotting it for $x \in [-2, 8]$, so that $f(x) \in [0, 25]$).

$$f(x) = \frac{1}{(x-3)^2+0.1} + \frac{1}{(x-2)^2+0.05} + 2$$

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    and to reference @J. M. isn't a mathematician's point, I do think the name comes from MATLAB.2017-07-19
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    see: https://www.mathworks.com/help/matlab/examples/function-functions.html#zmw57dd0e83592017-07-19
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i think any function $g(x)$ that is the derivative of a sigmoid function

$$ g(x) = f'(x) $$

where $f(x)$ may be any of the functions shown as examples of an S-shaped sigmoid function indicated in the Wikipedia article, any of those can be legitimately called a "hump function".