Geodesic
On some properties of a Fox function
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 203-211.

Voir la notice de l'article provenant de la source Math-Net.Ru

A partial case of a special Fox function is considered. Integral representation, power series representation, and asymptotic formulas are written out. The formulas of differentiation of the integer order, recurrent and integral relations are proved.
Keywords: Fox function, integral representation, asymptotics, recurrent relation, differentiation formula. 
@article{CHFMJ_2023_8_2_a3,
     author = {F. G. Khushtova},
     title = {On some properties of a {Fox} function},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {203--211},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a3/}
}
TY  - JOUR
AU  - F. G. Khushtova
TI  - On some properties of a Fox function
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2023
SP  - 203
EP  - 211
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a3/
LA  - ru
ID  - CHFMJ_2023_8_2_a3
ER  - 
%0 Journal Article
%A F. G. Khushtova
%T On some properties of a Fox function
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2023
%P 203-211
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a3/
%G ru
%F CHFMJ_2023_8_2_a3
F. G. Khushtova. On some properties of a Fox function. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 203-211. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a3/

[1] Kuznetsov D.S., Special functions, Higher school, Moscow, 1962 (In Russ.)

[2] Bateman G., Erdelyi A., Higher Transcendental Functions, v. 1, McGraw-Hill Book Company, New York, 1965

[3] Prudnikov A.P., Brychkov Yu.A., Marichev O.I., Integrals and series. Additional chapters, v. 3, Nauka, Moscow, 1986 (In Russ.) | MR

[4] Kilbas A. A., Saigo M., H-Transform. Theory and Applications, Chapman and Hall/CRC, Boca Raton, London, New York, Washington, 2004 | MR

[5] Mathai A. M., Saxena R. K., Haubold H. J., The H-function. Theory and Applications, Springer, New York, 2010 | MR | Zbl

[6] Khushtova F.G., “First boundary-value problem in the half-strip for a parabolic-type equation with Bessel operator and Riemann — Liouville derivative.”, Mathematical Notes, 99:6 (2016), 916–923 | DOI | DOI | MR | Zbl

[7] Khushtova F.G., “The second boundary-value problem in a half-strip for a parabolic-type equation with Bessel operator and Riemann — Liouville partial derivative”, Mathematical Notes, 103:103 (2018), 474–482 | DOI | DOI | MR

[8] Khushtova F.G., “Differentiation formulas and autotransformation formula for a partial case of the Fox function”, Reports of the Adyghe International Academy of Sciences, 20:4 (2020), 15–18 (In Russ.) | MR

[9] Marichev O.I., Method for calculating integrals from special functions (theory and tables of formulas), Science and technics, Minsk, 1978 (In Russ.) | MR

[10] Gradshtein I.S., Ryzhik I.M., Tables of integrals, sums, series and products, Fizmatlit, Moscow, 1963 (In Russ.) | MR