Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University2083310.14498/vsgtu1243Original ArticleExpansion of multiple series in infinite diagonalsKorneevAnton AStudent, Dept. of Mathematics & Physicskorneevant@bk.ruDoroshkevichOlga A(Ph.D. Phys. & Math.), Associate Professor, Dept. of Mathematics & Physicsodoroshkevich@bk.ruSholokhov Moscow State University for the Humanities15122013174586518022020Copyright © 2013, Samara State Technical University2013In this paper a method of summation of double absolutely convergent numerical series was obtained. This method was named the expansion of double numerical series in inﬁnite diagonals. The form of the expansion for symmetric and skew-symmetric general term of double series was established. This expansion was generalized to the case of multiple series. It was called the expansion of multiple numerical series in inﬁnite diagonals for two indices. The expansion of triple series in inﬁnite diagonals for two indices was generalized to the case of three indices.multiple seriesdouble seriesmethod of summation of multiple seriesinﬁnite diagonalsдвойной рядкратный рядметод суммирования кратных рядовбесконечные диагонали[Г. М. Фихтенгольц, Курс дифференциального и интегрального исчисления. Т. 2. СПб.: Лань, 2009. 800 с.][Я. С. Бугров, С. М. Никольский, Дифференциальное и интегральное исчисление. Т. 2. М.: Дрофа, 2004. 512 с.]