Analytic continuation of the Kampé de Fériet function and the general double Horn series. Issue 11 (2nd November 2022)

• Record Type: Journal Article
• Authors: Bezrodnykh, S. I.
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 11(2022)
• Page Start: 908
• Page End: 928
• Publication Date: 2022-11-02
• Subjects: Multiple hypergeometric functions -- Kampé de Fériet function -- Horn series -- analytic continuation; 33C65 -- 32D15 -- 33C90; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2056601
• Languages: English
• ISSNs: 1065-2469

Abstract

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.