Geodesic
Finding the Coefficients in the New Representation of the Solution of the Riemann--Hilbert Problem Using the Lauricella Function
Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 647-668

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

The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function $F_D^{(N)}$. The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.
Keywords: Riemann–Hilbert problem with piecewise constant data, Lauricella function $F_D^{(N)}$, Christoffel–Schwartz integral.
Mots-clés : Jacobi-type formula 
@article{MZM_2017_101_5_a1,
     author = {S. I. Bezrodnykh},
     title = {Finding the {Coefficients} in the {New} {Representation} of the {Solution} of the {Riemann--Hilbert} {Problem} {Using} the {Lauricella} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {647--668},
     publisher = {mathdoc},
     volume = {101},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a1/}
}
TY  - JOUR
AU  - S. I. Bezrodnykh
TI  - Finding the Coefficients in the New Representation of the Solution of the Riemann--Hilbert Problem Using the Lauricella Function
JO  - Matematičeskie zametki
PY  - 2017
SP  - 647
EP  - 668
VL  - 101
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a1/
LA  - ru
ID  - MZM_2017_101_5_a1
ER  - 
%0 Journal Article
%A S. I. Bezrodnykh
%T Finding the Coefficients in the New Representation of the Solution of the Riemann--Hilbert Problem Using the Lauricella Function
%J Matematičeskie zametki
%D 2017
%P 647-668
%V 101
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a1/
%G ru
%F MZM_2017_101_5_a1
S. I. Bezrodnykh. Finding the Coefficients in the New Representation of the Solution of the Riemann--Hilbert Problem Using the Lauricella Function. Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 647-668. http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a1/