Can you guess the functional form of the following curve
y is 0 at x= Infinite ; y is very small ( +ve near to zero) at x=0
Thanks and regards
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2 Answers
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There are many functions that fit your criteria, but it does look like Planck's Distribution. Which is of form:
$$f(x)=\frac{Ax^3}{e^{Bx}-1}$$ $x\in \mathbb R $ and $A$, $B$ constants
Look at this.
answered Aug 2, 2013 at 21:51
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Keep in mind that this much information doesn't specify the curve completely: there are several that will fit this definition and overall shape. One option is
$$\frac{2abx}{x^2+b^2}$$
where $a$ and $b$ are numbers that you can pick: $a$ will be the maximum height, and $b$ will be the $x$-value that it happens at.
One that decays a lot faster is
$$\frac ab xe^{1-\frac xb}$$
where $(a,b)$ is again the position of the top of the bump.
answered Aug 2, 2013 at 21:55