Re: Converting MeijerG to Special Function like ln(x+1) in Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg131550] Re: Converting MeijerG to Special Function like ln(x+1) in Mathematica?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 24 Aug 2013 04:20:14 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20130823093013.B21DC69EC@smc.vnet.net>

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 at 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 at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower University of Massachusetts 710 North Pleasant Street Amherst, MA 01003-9305

**References**:**Converting MeijerG to Special Function like ln(x+1) in Mathematica?***From:*amzoti <amzoti@gmail.com>