BesselK interpretation in Wolfram Alpha?

Questions
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1

Hi!

So I’ve gotten the expression above in an answer from Wolfram|Alpha. I don’t know how to interpret the meaning of the superscript. For example “BesselK(3,4)” would mean the modified Bessel function of the second kind, of order 3, evaluated at 4. So what does the superscript means? some sort of derivative? Why are there two values in the superscript?

The output comes from the following query, if that helps:

integral log(x)**2/x*exp(-7x - 5/x) from 0 to inf

First post here. Please let me know if I’ve posted this question in the wrong place.

2

Often that notation can mean the second derivative of the function with respect to the first argument.

For example, in a fresh Wolfram|Alpha window I enter

D[ g[x,y],{x,2}]

which indicates taking the second derivative of g(x,y) with respect to x

then it promptly returns (approximately formatted here)

g^(2,0)(x,y)

If in a fresh Wolfram|Alpha window I enter

integral log(x)*2/x exp(-7x - 5/x) from 0 to inf

then it promptly returns

-2 log(7/5) K0(2 Sqrt(35))

and tells me that K0(x) is the modified Bessel function of the second kind.

3

Hi Bill, thanks for the reply!

Ok, then I understand the superscript notation. second derivative w.r.t. the order in this case I guess.

I see now that I included the wrong query in my original question. It is when the logarithm is raised to the power of two that the second derivative shows up.

integral log(x)2*1/x exp(-7x -5/x) from 0 to inf