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SOURCE:    Almanac of Modern Science and Education. Tambov: Gramota, 2016. № 7. P. 105-108.
SCIENTIFIC AREA:    Physical-Mathematical Sciences
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Tarasov Vasily Evgen'evich
Lomonosov Moscow State University

Abstract. The article defines a new notion of discrete mathematics - exact finite differences. A linear difference operator is called an exact finite difference of the order k , if the action of this operator within the space of entire functions coincides with the action of a derivative of the order k . Correspondence between differential calculus and calculus of finite differences is seen not in passage to the limit at the discretization interval tenting to zero, but in the subordination of the mathematical operators of these two theories in many cases to the same rules. The paper offers a brief overview of the basic properties of exact finite differences in the space of entire functions.
Key words and phrases: конечные разности, нестандартная дискретизация, точная дискретизация, точные конечные разности, разностный оператор дробного порядка, finite differences, non-standard sampling, exact sampling, exact finite differences, difference operator of fraction order
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