Geodesic
Formula for analytic continuation of the Kamp\'e de F\'eriet hypergeometric function
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 97-106

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We apply the method of Burchnall—Chaundy operators to the study of expansion formulas for the Kampé de Férriet hypergeometric function $F_{1:1;1}^{0:3;3} [x,y]$. Using the obtained operator identities, we derive 14 expansion formulas. A new group of Euler-type integral representations for the Kampé de Férriet hypergeometric function $F_{1:1;1}^{0:3;3} [x,y]$ is found and its analytic continuation is constructed.
Keywords: Kampé de Férriet hypergeometric function, Bourchnall–Chaundy operator, integral representation, expansion formula, analytic continuation. 
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     author = {A. Hasanov and T. K. Yuldashev},
     title = {Formula for analytic continuation of the {Kamp\'e} de {F\'eriet} hypergeometric function},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {97--106},
     publisher = {mathdoc},
     volume = {217},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2022_217_a10/}
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A. Hasanov; T. K. Yuldashev. Formula for analytic continuation of the Kamp\'e de F\'eriet hypergeometric function. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 97-106. http://geodesic.mathdoc.fr/item/INTO_2022_217_a10/