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/}
}
TY  - JOUR
AU  - Ichinobe, Kunio
TI  - On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2005
SP  - 435
EP  - 458
VL  - 14
IS  - 3
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2005_6_14_3_435_0/
LA  - en
ID  - AFST_2005_6_14_3_435_0
ER  - 
%0 Journal Article
%A Ichinobe, Kunio
%T On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2005
%P 435-458
%V 14
%N 3
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2005_6_14_3_435_0/
%G en
%F AFST_2005_6_14_3_435_0
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