Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation

Hasanov A., Ergashev T.G., Djuraev N.

O‘zbekiston matematika jurnali · 2025-yil

Annotatsiya

In this paper, hypergeometric function of Lauricella $F_{A}^{(n)}$ has been investigated. The new properties of which are established and applied to the solution of the Dirichlet problem for the three-dimensional degenerate elliptic equation. Fundamental solutions of the named equation are expressed through the Lauricella hypergeometric function in three variables and an explicit solution of the Dirichlet problem in the first octant is written out through the Appell hypergeometric function $F_2$. A limit theorem for calculating the value of a function of many variables is proved, and formulas for their transformation are established. These results are used to determine the order of singularity of fundamental solutions and to prove the truth of the solution to the Dirichlet problem. The uniqueness of the solution to the Dirichlet problem is proved by the extremum principle for elliptic equations.

Maqola ma’lumotlari
MualliflarHasanov A., Ergashev T.G., Djuraev N.
JurnalO‘zbekiston matematika jurnali
NashriyotЎзбекистон Республикаси ФА Математика институти
ISSN2010-7269
Nashr sanasi2025-09-06
Jild69
Son3
Betlar73-82
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.29229/uzmj.2025-3-7
Indeksga qo‘shilgan2026-08-26

DOI: 10.29229/uzmj.2025-3-7 · Maqolaning asl sahifasi

Kalit so‘zlar

Appell and Lauricella hypergeometric functions, three-dimensional degenerate elliptic equation, PDE-systems of hypergeometric type, fundamental solution, Dirichlet problem

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAHasanov A., Ergashev T.G., & Djuraev N. (2025). Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation. O‘zbekiston matematika jurnali, 69(3), 73-82. https://doi.org/10.29229/uzmj.2025-3-7
GOST (OAK)Hasanov A., Ergashev T.G., Djuraev N. Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 73-82. – DOI: 10.29229/uzmj.2025-3-7.
MLAHasanov A., Ergashev T.G., and Djuraev N. “Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation.” O‘zbekiston matematika jurnali, 69(3), 73-82, 2025. https://doi.org/10.29229/uzmj.2025-3-7
ChicagoHasanov A., Ergashev T.G., and Djuraev N. “Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation.” O‘zbekiston matematika jurnali, 69(3), 73-82 (2025). https://doi.org/10.29229/uzmj.2025-3-7
HarvardHasanov A., Ergashev T.G., and Djuraev N (2025) ‘Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation’, O‘zbekiston matematika jurnali, 69(3), 73-82. https://doi.org/10.29229/uzmj.2025-3-7
BibTeX
@article{hasanova2025,
  title = {Lauricella hypergeometric function $F_{A}^{(n)}$ with applications to the solving Dirichlet problem for three-dimensional degenerate elliptic equation},
  author = {Hasanov A. and Ergashev T.G. and Djuraev N.},
  journal = {O‘zbekiston matematika jurnali},
  year = {2025},
  volume = {69},
  number = {3},
  pages = {73-82},
  doi = {10.29229/uzmj.2025-3-7},
  url = {https://doi.org/10.29229/uzmj.2025-3-7}
}

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