Geodesic
Operator hypergeometric functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 37-45

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We consider operator hypergeometric functions ${_1}F_2(\cdot)$ and ${_2}F_3(\cdot)$ constructed by an unbounded operator. Using these functions, we solve Cauchy problems for singular integro-differential equations. A new pair of similar operators is given.
Keywords: transformation operator, Bessel operator function, Bessel–Struve operator function, operator hypergeometric function, integro-differential equation. 
@article{INTO_2020_174_a3,
     author = {A. V. Glushak},
     title = {Operator hypergeometric functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {37--45},
     publisher = {mathdoc},
     volume = {174},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_174_a3/}
}
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A. V. Glushak. Operator hypergeometric functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 174 (2020), pp. 37-45. http://geodesic.mathdoc.fr/item/INTO_2020_174_a3/