Geodesic
On the Analytic Complexity of Hypergeometric Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 267-275

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Hypergeometric functions of several variables resemble functions of finite analytic complexity in the sense that the elements of both classes satisfy certain canonical overdetermined systems of partial differential equations. Otherwise these two sets of functions are very different. We investigate the relation between the two classes of functions and compute the analytic complexity of certain bivariate hypergeometric functions. 
@article{TM_2017_298_a15,
     author = {T. M. Sadykov},
     title = {On the {Analytic} {Complexity} of {Hypergeometric} {Functions}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {267--275},
     publisher = {mathdoc},
     volume = {298},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_298_a15/}
}
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T. M. Sadykov. On the Analytic Complexity of Hypergeometric Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and its applications, Tome 298 (2017), pp. 267-275. http://geodesic.mathdoc.fr/item/TM_2017_298_a15/