Title | On summation of series by means of solution of the Dirichlet problem for rectangle |
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Authors | E. S. Alekseeva^{1}, A. E. Rassadin^{2}^{1}Laboratory of infinite-dimensional analysis and mathematical physics, faculty of mechanics and mathematics, Lomonosov Moscow State University ^{2}National Research University "Higher School of Economics" |

Annotation | In the article, method of receiving of new identities for the complete elliptic integral of the first kind has been presented. The corner stone of this method is construction of exact solution of the Dirichlet problem for rectangle under special choice of boundary condition. Further one ought to calculate values of this exact solution in specially chosen internal points of this rectangle and to compare them vith values of solution of the same problem obtained in the framework of separation of variables in the same points. Amount of these new identities is determined by store of known values of used exact solution. |

Keywords | conformal mapping, Jacobian elliptic functions, modulus of complete elliptic integral, inverse function, numerical and functional series |

Citation | Alekseeva E. S., Rassadin A. E. ''On summation of series by means of solution of the Dirichlet problem for rectangle'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, October 8-11, 2020). Saransk: SVMO Publ, 2020. - pp. 142-147. Available at: http://conf.svmo.ru/files/2020/papers/article02.pdf. - Date of access: 18.10.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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