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Topic: Converting MeijerG to Special Function like ln(x+1) in Mathematica?
Replies: 1   Last Post: Aug 24, 2013 4:14 AM

 Murray Eisenberg Posts: 2,105 Registered: 12/6/04
Re: Converting MeijerG to Special Function like ln(x+1) in Mathematica?
Posted: Aug 24, 2013 4:14 AM

You could try FunctionExpand, possibly with optional 2nd argument
putting assumptions on x. However, your purported result in the first
example has a syntax error -- unbalanced parentheses -- which I'm going
to assume should actually be:

(1/2 Sqrt[Pi]) x^3 Exp[-x/2] (BesselK[0, x/2] + BesselK[1, x/2])

And I don't think that's the same thing as your

MeijerG[{{}, {5/2}}, {{2, 3}, {}}, x]

(which is correct Mathematica syntax for a MeijerG that, if I understand
what you wrote, is what you want). In fact, plotting the two functions
reveals the difference.

On Aug 23, 2013, at 5:30 AM, amzoti <amzoti@gmail.com> wrote:

> Does Mathematica have a similar function to this?
>
> convert(MeijerG([[],[5/2]],[[2,3],[]],x),StandardFunctions);
>
> which results in: (1/(2 Sqrt[Pi]) x^3 Exp[-x/2] (BesselK[0,x/2]+BesselK[1,x/2]).
>
> or
>
> convert(ln(1+x),MeijerG,include=elementary);
>
> You can see what the result would be here:

http://en.wikipedia.org/wiki/Meijer_G-function
>
> I found this nice list of special functions on the Mathematica web

site (http://functions.wolfram.com/HypergeometricFunctions/MeijerG/03/01/03/23/) and can look it up, but would rather be able to go in each direction by typing a command.
>
> Is there a way to do this in Mathematica?

---
Murray Eisenberg murray@math.umass.edu
Mathematics & Statistics Dept.
University of Massachusetts
710 North Pleasant Street
Amherst, MA 01003-9305