On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 435-458. 
@article{AFST_2005_6_14_3_435_0,
     author = {Ichinobe, Kunio},
     title = {On the relation between the {Borel} sum and the classical solution of the {Cauchy} problem for certain partial differential equations},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {435--458},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {3},
     year = {2005},
     mrnumber = {2172586},
     zbl = {1090.35052},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_3_435_0/}
}
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Ichinobe, Kunio. On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 435-458. http://www.numdam.org/item/AFST_2005_6_14_3_435_0/

[Bal] Balser (W.). - From Divergent Power Series to .Analytic Functions , Springer Lecture Notes, No. 1582 (1994). | MR | Zbl

[Ich 1] Ichinobe ( K.). - The Borel Sum of Divergent Barnes Hypergeometric Series and its Application to a Partial Differential Equation, Publ. Res. Inst. Math. Sci. 37, No. 1, p. 91-117 (2001). | MR | Zbl

[Ich 2] -, Integral Representation for Borel Sum of Divergent Solution to a certain non-Kowalevski type Equation, Publ. Res. Inst. Math. Sci. 39, No. 4, p. 657-693 (2003). | MR | Zbl

[LMS] Lutz (D.) , Miyake ( M.), Schäfke (R.). - On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J. 154, p. 1-29 (1999). | MR | Zbl

[Luk] Luke (Y.L.). - The Special Functions and Their Approximations , Vol I Academic Press , 1969. | MR | Zbl

[Miy] Miyake (M.). - Borel summability of divergent solutions of the Cauchy problem to non-Kowalevskian equations, Partial differential equations and their applications (Wuhan, 1999), p. 225-239, World Sci. Publishing River Edge, NJ ( 1999). | MR | Zbl

[MS] Mathai (A.M. ) , Saxena ( R.K.). - Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer Lecture Notes. No. 348, ( 1973). | MR | Zbl