h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Could anyone tell me what the first order differential of a stretched expontential function is algebriacly.

I ask not for myself, (in which case you would have to be not only friendly but would have talk really slowly for a very long time) but for a friend of mine, who understands these things.

Apparently it would make his graphs much more pretty and it peeves him that he can only do these things numerically.

Drinks, cakes, much adulation alround if you could provide an answer, or explaination if a solution is too difficult to come by

Peanut

what's a 'stretched' exponential function?

Differentials of exponentials are dead easy otherwise...

OK, it's as described here
http://en.wikipedia.org/wiki/Stretched_exponential_function

gotta at the moment. Will think some more on it later.

Ach, crivens. Not hard to doo, but you have to decompose everything. Lemme see if I can still do it. Warning, grotty formulas ahead.

f(t) = exp{-(t/k)^b} = exp{-exp(b.ln(t/k))} = exp(g(t))

then f'(t) = g'(t) exp(g(t))

Compute g'(t) = -(b/k)*(t/k)^(b-1) using the usual rules for the differential of exponentials.

Put everything together and you get:


f'(t) = -(b/k)*(t/k)^(b-1) exp{-(t/k)^b}.


And you can check that the formula is true in the classical case b=1 (which was not the case of my previous few results ) This is no warranty that the result is true, but it helps against gross errors.

Toybox,

There were ohhs and ahhs, followed by 'I see' down the phone then an explitive as as subscribtion had lapsed so he couldn't try it out at home to make his graphs pretty

Many thanks, much adulation, and drinks of choice are yours,

Peanut

Explaining that on the phone? A most gallant task

Took one look and guided him to page while on phone

Ha, sissies

In my case, so true, that sort of thing makes me go weak at the knees

I enjoyed 'ach crivens' but gave up thereafter.

B

*wanders in late, as usual*

Subscription has lapsed? Is that subscription for some package that does the pretty graphing?

If so, you (or perhaps he) may wish to check out http://www.sagemath.org, which is a free and open source alternative to stuff I can't afford, like Mathematica. Take that, Wolfram.

Found out about sagemath.org at last month's nerd-fest, I mean, math conference.


HN