Translation, Creation and Annihilation of Poles and Zeros with the Biernacki and Ruscheweyh Operators, Acting on Meijer's G-Functions

Abstract EN

Meijer's G-functions are studied by the Biernacki and Ruscheweyh operators.

These operators are special cases of the Erdélyi-Kober operators (for m=1).

The effect of operators on Meijer's G-functions can be shown as the change in the distribution of poles and zeros on the complex plane.

These poles and zeros belong to the integrand, a ratio of gamma functions, defining the Meijer's G-function.

Displacement in position and increasing or decreasing in number of poles and zeroes are expressed by the transporter, creator, and annihilator operators.

With special glance, three basic univalent Meijer's G-functions, Koebe, and convex functions are considered.