Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values





Specialized values

Cases with arbitrary {m,n,p,q}

Case with fixed a1,...,ap

>
>

Case {m,n,p,q}={0,n,n,n}

>

Case {m,n,p,q}={1,0,0,q}

>

Case {m,n,p,q}={1,1,1,q}

>

Case {m,n,p,q}={1,p,p,q}

>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,n,n,n}

>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,n,n,n+1}

>
>
>
>
>
>

Case {m,n,p,q}={m,0,m,m}

>

Case {m,n,p,q}={m,0,0,m}

>

Case {m,n,p,q}={m,1,m,m}

>
>
>
>
>
>

Case {m,n,p,q}={q,1,p,q}

>
>

Cases with m==0

Case {m,n,p,q}={0,0,0,0}

>

Case {m,n,p,q}={0,1,1,0}

>

Case {m,n,p,q}={0,1,1,1}

>
>
>
>

Case {m,n,p,q}={0,1,2,0}

>
>
>
>
>

Case {m,n,p,q}={0,1,2,1}

>
>
>
>

Case {m,n,p,q}={0,1,2,2}

>

Case {m,n,p,q}={0,1,3,0}

>
>
>
>

Case {m,n,p,q}={0,1,3,1}

>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={0,1,3,2}

>

Case {m,n,p,q}={0,1,3,3}

>

Case {m,n,p,q}={0,1,4,0}

>
>

Case {m,n,p,q}={0,2,2,0}

>
>
>

Case {m,n,p,q}={0,2,2,1}

>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={0,2,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={0,2,3,0}

>
>

Case {m,n,p,q}={0,2,3,1}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={0,2,3,2}

>

Case {m,n,p,q}={0,2,3,3}

>

Case {m,n,p,q}={0,2,4,0}

>
>

Case {m,n,p,q}={0,2,5,1}

>
>

Case {m,n,p,q}={0,3,3,0}

>

Case {m,n,p,q}={0,3,3,1}

>
>
>
>
>
>

Case {m,n,p,q}={0,3,3,2}

>

Case {m,n,p,q}={0,3,3,3}

>
>
>

Case {m,n,p,q}={0,3,4,0}

>
>
>

Case {m,n,p,q}={0,3,4,2}

>
>
>
>
>
>

Case {m,n,p,q}={0,3,4,1}

>
>
>

Case {m,n,p,q}={0,3,6,2}

>
>

Case {m,n,p,q}={0,4,4,0}

>

Case {m,n,p,q}={0,4,4,2}

>
>
>

Case {m,n,p,q}={0,4,5,1}

>

Case {m,n,p,q}={0,4,5,3}

>

Cases with m==1

Case {m,n,p,q}={1,0,0,1}

>

Case {m,n,p,q}={1,0,0,2}

>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,0,0,3}

>
>
>
>

Case {m,n,p,q}={1,0,0,4}

>
>
>
>

Case {m,n,p,q}={1,0,1,1}

>
>
>
>

Case {m,n,p,q}={1,0,1,2}

>
>
>
>

Case {m,n,p,q}={1,0,1,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,0,2,2}

>

Case {m,n,p,q}={1,0,2,3}

>

Case {m,n,p,q}={1,0,3,3}

>

Case {m,n,p,q}={1,1,1,1}

>

Case {m,n,p,q}={1,1,1,2}

>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,1,1,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,1,2,1}

>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,1,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,1,2,3}

>
>
>
>
>
>

Case {m,n,p,q}={1,1,2,4}

>
>
>
>
>
>

Case {m,n,p,q}={1,1,4,2}

>
>
>
>
>
>

Case {m,n,p,q}={1,1,3,1}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,1,3,2}

>
>
>
>
>

Case {m,n,p,q}={1,1,3,3}

>

Case {m,n,p,q}={1,2,2,1}

>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,2,3}

>
>
>
>
>
>

Case {m,n,p,q}={1,2,2,4}

>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,3,5}

>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,4,2}

>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,3,1}

>
>
>
>
>
>
>

Case {m,n,p,q}={1,2,3,2}

>
>

Case {m,n,p,q}={1,2,3,3}

>
>

Case {m,n,p,q}={1,3,3,1}

>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,3,3,2}

>

Case {m,n,p,q}={1,3,3,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={1,3,4,2}

>
>
>
>
>
>

Case {m,n,p,q}={1,4,4,2}

>
>
>
>
>
>

Case {m,n,p,q}={1,4,4,4}

>
>
>
>
>
>
>
>
>
>
>
>
>

Cases with m==2

Case {m,n,p,q}={2,0,0,2}

>
>
>
>

Case {m,n,p,q}={2,0,0,3}

>
>

Case {m,n,p,q}={2,0,0,4}

>
>

Case {m,n,p,q}={2,0,1,2}

>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,0,1,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,0,1,4}

>
>

Case {m,n,p,q}={2,0,1,5}

>
>
>
>

Case {m,n,p,q}={2,0,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,0,2,3}

>

Case {m,n,p,q}={2,0,2,4}

>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,0,3,3}

>

Case {m,n,p,q}={2,1,1,2}

>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,1,1,3}

>
>
>
>
>
>
>

Case {m,n,p,q}={2,1,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,1,2,3}

>
>

Case {m,n,p,q}={2,1,2,4}

>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,1,3,2}

>
>
>
>
>
>

Case {m,n,p,q}={2,1,3,3}

>
>

Case {m,n,p,q}={2,1,4,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,1,5,3}

>
>
>
>
>

Case {m,n,p,q}={2,2,2,2}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,2,2,3}

>

Case {m,n,p,q}={2,2,2,4}

>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,2,3,2}

>

Case {m,n,p,q}={2,2,3,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,2,3,5}

>
>
>
>
>

Case {m,n,p,q}={2,2,4,2}

>
>
>
>
>
>

Case {m,n,p,q}={2,2,4,6}

>
>
>

Case {m,n,p,q}={2,2,5,3}

>
>
>
>
>

Case {m,n,p,q}={2,3,3,2}

>

Case {m,n,p,q}={2,3,3,3}

>

Case {m,n,p,q}={2,3,4,2}

>
>
>
>
>
>
>
>

Case {m,n,p,q}={2,4,5,3}

>

Cases with m==3

Case {m,n,p,q}={3,0,0,3}

>
>

Case {m,n,p,q}={3,0,0,4}

>
>
>
>
>
>

Case {m,n,p,q}={3,0,1,3}

>
>
>
>
>
>

Case {m,n,p,q}={3,0,1,4}

>
>

Case {m,n,p,q}={3,0,1,5}

>
>
>

Case {m,n,p,q}={3,0,2,3}

>

Case {m,n,p,q}={3,0,2,4}

>
>
>
>
>
>

Case {m,n,p,q}={3,0,2,6}

>
>

Case {m,n,p,q}={3,0,2,6}

>
>
>

Case {m,n,p,q}={3,1,1,3}

>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={3,1,2,3}

>

Case {m,n,p,q}={3,1,2,4}

>
>
>
>
>
>
>

Case {m,n,p,q}={3,1,3,3}

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={3,2,2,3}

>

Case {m,n,p,q}={3,2,2,4}

>
>
>
>
>
>
>
>

Case {m,n,p,q}={3,2,3,3}

>

Case {m,n,p,q}={3,3,3,3}

>
>

Case {m,n,p,q}={3,3,4,4}

>
>

Cases with m==4

Case {m,n,p,q}={4,0,0,4}

>
>

Case {m,n,p,q}={4,0,1,5}

>

Case {m,n,p,q}={4,0,2,4}

>
>
>

Case {m,n,p,q}={4,0,3,5}

>

Case {m,n,p,q}={4,1,2,4}

>
>
>
>
>
>
>

Case {m,n,p,q}={4,1,4,4}

>
>
>
>
>
>
>
>
>
>
>
>

Case {m,n,p,q}={4,2,3,5}

>

Cases with m==5

Case {m,n,p,q}={5,0,0,6}

>
>
>





© 1998-2014 Wolfram Research, Inc.