Can you guess the functional form of the following curve

y vs x

y is 0 at x= Infinite ; y is very small ( +ve near to zero) at x=0

Thanks and regards


2 Answers 2


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.


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


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.


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