On Transformations of A-Hypergeometric Functions Academic Article

abstract

• We propose a systematic study of transformations of $A$-hypergeometric functions. Our approach is to apply changes of variables corresponding to automorphisms of toric rings, to Euler-type integral representations of $A$-hypergeometric functions. We show that all linear $A$-hypergeometric transformations arise from symmetries of the corresponding polytope. As an application of the techniques developed here, we show that the Appell function $F_4$ does not admit a certain kind of Euler-type integral representation.

authors

• Matusevich, Laura

published proceedings

• FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA

author list (cited authors)

• Forsgard, J., Matusevich, L. F., & Sobieska, A.

citation count

• 0

complete list of authors

• Forsgard, Jens||Matusevich, Laura Felicia||Sobieska, Aleksandra

publication date

• March 2019

publisher

• Division of Functional Equations, The Mathematical Society of Japan (JST)  Publisher

published in

• Funkcialaj Ekvacioj, Serio Internacia  Journal

keywords

• Euler Type Integrals
• Hypergeometric Functions
• Hypergeometric Transformations

Digital Object Identifier (DOI)

• 10.1619/fesi.62.319

start page

• 319

end page

• 336

volume

• 62

issue

• 3

URL

• http://dx.doi.org/10.1619/fesi.62.319