<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We first introduce a notation for multiple (<italic>n</italic> ≥ 3) <italic>q</italic>-hypergeometric functions, where negative values of summation indices are allowed. Then we extend the notation for <italic>q</italic>-Horn functions to include tilde values corresponding to powers of 2. Karlssons reduction formulas are correspondingly <italic>q</italic>-deformed by using these notations. A formula for sums of inverse <italic>q</italic>-shifted factorials is used to find further formulas. The second part of the paper is devoted to convergence aspects for <italic>q</italic>-Horn functions and ’abnormal’ <italic>q</italic>-Horn functions. It turns out that some simple estimates for convergence can be made in the <italic>q</italic>-case, these are then supplemented with tables of numerical values. It is shown that the convergence regions are significantly increased in the <italic>q</italic>-case, and we compare with convergence regions in the ordinary case.</p>
</abstract>

We first introduce a notation for multiple (n ≥ 3) q-hypergeometric functions, where negative values of summation indices are allowed. Then we extend the notation for q-Horn functions to include tilde values corresponding to powers of 2. Karlssons reduction formulas are correspondingly q-deformed by using these notations. A formula for sums of inverse q-shifted factorials is used to find further formulas. The second part of the paper is devoted to convergence aspects for q-Horn functions and ’abnormal’ q-Horn functions. It turns out that some simple estimates for convergence can be made in the q-case, these are then supplemented with tables of numerical values. It is shown that the convergence regions are significantly increased in the q-case, and we compare with convergence regions in the ordinary case.

Several new aspects on <italic>q</italic>-Horn and related triple functions in the spirit of Karlsson

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Several new aspects on -Horn and related triple functions in the spirit of Karlsson

We first introduce a notation for multiple (n ≥ 3) q-hypergeometric functions, where negative values of summation indices are allowed. Then we extend the...

Several new aspects on q-Horn and related triple functions in the spirit of Karlsson

Published Online: May 27, 2024

Page range: 155 - 182

Received: Feb 09, 2023

Accepted: Apr 18, 2023

DOI: https://doi.org/10.2478/auom-2024-0009

Keywords
-Horn functions, convergence region, notation

© 2024 Thomas Ernst, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Several new aspects on q-Horn and related triple functions in the spirit of Karlsson

Published Online: May 27, 2024

Page range: 155 - 182

Received: Feb 09, 2023

Accepted: Apr 18, 2023

DOI: https://doi.org/10.2478/auom-2024-0009

Keywords-Horn functions, convergence region, notation

© 2024 Thomas Ernst, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
-Horn functions, convergence region, notation