Analytic continuation of the Kampé de Fériet function and the general double Horn series

Abstract

For the Kampé de Fériet function, such analytic continuation formulas are obtained that allow one to represent this function as exponentially converging hypergeometric series in the complement to the convergence domain of the original series. This result has been obtained using the found formulas for the analytic continuation of the Horn series in two variables.

Keywords:

• Multiple hypergeometric functions
• Kampé de Fériet function
• Horn series
• analytic continuation

AMS CLASSIFICATIONS:

• 33C65
• 32D15
• 33C90

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).