MEIJERG _ _ _ _ _ _ _ _ _ _ _ _ operator

The MeijerG operator provides simplifications for Meijer's G function. The simplifications are performed towards polynomials, elementary or special functions or (generalized) hypergeometric functions.

The MeijerG operator is included in the package specfn2.

syntax:

The first element of the lists has to be the list containing the first group (mostly called ``m'' and ``n'') of parameters. This passes the four parameters of a Meijer's G function implicitly via the length of the lists.

examples:

load specfn2;

MeijerG({{},1},{{0}},x); 

  heaviside(-x+1)


MeijerG({{}},{{1+1/4},1-1/4},(x^2)/4) * sqrt pi;
 


                  2
  sqrt(2)*sin(x)*x
  ------------------
      4*sqrt(x)

Many well-known functions can be written as G functions, e.g. exponentials, logarithms, trigonometric functions, Bessel functions and hypergeometric functions. The formulae can be found e.g. in

A.P.Prudnikov, Yu.A.Brychkov, O.I.Marichev: Integrals and Series, Volume 3: More special functions, Gordon and Breach Science Publishers (1990).