Geodesic
Jacobi-Type Differential Relations for the Lauricella Function $F_D^{(N)}$
Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 832-847

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For the generalized Lauricella hypergeometric function $F_D^{(N)}$, Jacobi-type differential relations are obtained and their proof is given. A new system of partial differential equations for the function $F_D^{(N)}$ is derived. Relations between associated Lauricella functions are presented. These results possess a wide range of applications, including the theory of Riemann–Hilbert boundary-value problem.
Keywords: generalized Lauricella hypergeometric function, Jacobi-type differential relation, Jacobi identity, Gauss function, Christoffel–Schwarz integral. 
@article{MZM_2016_99_6_a2,
     author = {S. I. Bezrodnykh},
     title = {Jacobi-Type {Differential} {Relations} for the {Lauricella} {Function} $F_D^{(N)}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {832--847},
     publisher = {mathdoc},
     volume = {99},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a2/}
}
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S. I. Bezrodnykh. Jacobi-Type Differential Relations for the Lauricella Function $F_D^{(N)}$. Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 832-847. http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a2/