Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Meijer-G/Fox-H Representation-Based Calculus |  |
m,n
G
p,q
a 1 a n a n+1 a p |
b 1 b m b m+1 b q |
1
2π
∫
ℒ
Γ(s+)Γ(1--s)
m
∏
k=1
b
k
n
∏
k=1
a
k
p
∏
k=n+1
a
k
q
∏
k=m+1
b
k
-s
z
and
m,n
H
p,q
( a 1 α 1 a n α n ( a n+1 α n+1 a p α p |
( b 1 β 1 b m β m ( b m+1 β m+1 b q β q |
1
2π
∫
ℒ
m
∏
j=1
b
j
β
j
n
∏
i=1
a
i
α
i
p
∏
i=n+1
a
i
α
i
q
∏
j=m+1
b
j
β
j
-s
z
Note that reduces to when the are all equal to one.
m,n
H
p,q
m,n
G
p,q
α
i
Much of the utility of these functions stems from the fact that a huge group of algebraic and special functions can be written as special cases of them when appropriate choices of the parameters are taken.
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