Geodesic
Expansion formulas for hypergeometric functions of two variables
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 80-97

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In the theory of hypergeometric functions, an important role is played by expansion formulas that allows one to express hypergeometric functions of several variables as infinite sums of products of several hypergeometric functions of one variable. In this paper, for hypergeometric functions of two variables, we introduce new symbolic Burchnall–Chaundy operators, examine their properties, and construct some expansions.
Keywords: hypergeometric function, expansion formula, symbolic form, Burchnall operator, Chaundy operator. 
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     author = {T. G. Ergashev},
     title = {Expansion formulas for hypergeometric functions of two variables},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--97},
     publisher = {mathdoc},
     volume = {201},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_201_a6/}
}
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T. G. Ergashev. Expansion formulas for hypergeometric functions of two variables. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 80-97. http://geodesic.mathdoc.fr/item/INTO_2021_201_a6/