Geodesic
The discrete analog of the Newton--Leibniz formula in the problem of summation over simplex lattice points
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 503-508

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Definition of the discrete primitive function is introduced in the problem of summation over simplex lattice points. The discrete analog of the Newton–Leibniz formula is found.
Keywords: summation of functions, discrete primitive function, discrete analog of the Newton–Leibniz formula. 
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     author = {Evgeniy K. Leinartas and Olga A. Shishkina},
     title = {The discrete analog of the {Newton--Leibniz} formula in the problem of summation over simplex lattice points},
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Evgeniy K. Leinartas; Olga A. Shishkina. The discrete analog of the Newton--Leibniz formula in the problem of summation over simplex lattice points. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 503-508. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a12/