hyperbolic distribution

Hey folks, remember me? I had that problem with the exponential
function. In continuing to work on that, I have realized that I
actually need an asymmetric spike, one with the left side pulled up and
out. I surfed the net and found something called the "hyperbolic
distribution," a variation on the exponential function. It is at

http://www.2dcurves.com/exponential/exponentialhd.html

This is precisely what I need. However, it is also very complex. The
initial expression is not much more than the exponential function, but
it is expressed in terms of the Bessel function of the second kind,
which is expressed in terms of the Bessel function of the first kind
which is expressed in terms of the Gamma function. All said and done,
the resulting equation is fantastically lengthy. Is all of this really
necessary? I can cope with it if I have to, but this is part of
something that will be published. I don't want to find out later that I
provided a mathematical monster when something much more simple would
have sufficed.

In my initial posts here, I thought I might have been intruding into
something that was more or less a private professional club for
mathematicians. I'm now suspecting that you folks are pretty
accommodating and even enjoy helping lost souls such as myself. If I'm
on the wrong track, somebody better say so. Remember the story about
Casey Jones ... (My background in math would be pretty limited in
comparison to the rest of you; I wouldn't have anything to contribute.
I would just have a lot of questions.)

Martin

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