Geodesic
Expansion of multiple series in infinite diagonals
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 58-65.

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In 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.
Keywords: multiple series, double series, method of summation of multiple series, infinite diagonals. 
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A. A. Korneev; O. A. Doroshkevich. Expansion of multiple series in infinite diagonals. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 58-65. http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a4/

[1] G. M. Fikhtengol'ts, Course of differential and integral calculus, v. 2, Lan', St. Petersburg, 2009, 800 pp.

[2] Ya. S. Bugrov, S. M. Nikol'sky, Differential and integral calculus, v. 2, Drofa, Moscow, 2004, 512 pp.