Journal of Inequalities and Applications

Table 4 The effect of the two-tuple Erdélyi-Kober operators on the Meijer's $G_{p, q + 1}^{1, p}$ -function (p = q = 1)

From: Fractional differintegral transformations of univalent Meijer's G-functions

Operators	Conditions	Transformation
$I_{1, 1}^{a_{3} - 1, b_{3} - a_{3}} I_{1, 1}^{a_{2} - 1, b_{2} - a_{2}}$	b₂ >a₂ and b₃ >a₃	$G_{1, 2}^{1, 1} \to G_{3, 4}^{1, 3} [_{0, 1 - b_{1}, 1 - b_{2}, 1 - b_{3}}^{1 - a_{1}, 1 - a_{2}, 1 - a_{3}} \| - z]$
$D_{1, 1}^{b_{3} - 1, a_{3} - b_{3}} I_{1, 1}^{a_{2} - 1, b_{2} - a_{2}}$	b₂ >a₂ and b₃ <a₃	$G_{1, 2}^{1, 1} \to G_{3, 4}^{1, 3}$
$I_{1, 1}^{a_{3} - 1, b_{3} - a_{3}} D_{1, 1}^{b_{2} - 1, a_{2} - b_{2}}$	b₂ <a₂ and b₃ >a₃	$G_{1, 2}^{1, 1} \to G_{3, 4}^{1, 3}$
$D_{1, 1}^{b_{3} - 1, a_{3} - b_{3}} D_{1, 1}^{b_{2} - 1, a_{2} - b_{2}}$	b₂ <a₂ and b₃ <a₃	$G_{1, 2}^{1, 1} \to G_{3, 4}^{1, 3}$

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