From: Fractional differintegral transformations of univalent Meijer's G-functions
Operators
Conditions
Transformation
I 1 , 1 a 3 - 1 , b 2 - a 3 I 1 , 1 a 2 - 1 , b 1 - a 2
b1 >a2 and b2 >a3
G 1 , 1 1 , 1 → G 3 , 3 1 , 3 [ 0 , 1 − b 1 , 1 − b 2 1 − a 1 , 1 − a 2 , 1 − a 3 | − z ]
D 1 , 1 b 2 - 1 , a 3 - b 2 I 1 , 1 a 2 - 1 , b 1 - a 2
b1 >a2 and b2 <a3
G 1 , 1 1 , 1 → G 3 , 3 1 , 3
I 1 , 1 a 3 - 1 , b 2 - a 3 D 1 , 1 b 1 - 1 , a 2 - b 1
b1 <a2 and b2 >a3
D 1 , 1 b 2 - 1 , a 3 - b 2 D 1 , 1 b 1 - 1 , a 2 - b 1
b1 <a2 and b2 <a3