Finite differences | Non-Newtonian calculus | Linear operators in calculus | Mathematical tables | Mathematical analysis

Indefinite sum

In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by or , is the linear operator, inverse of the forward difference operator . It relates to the forward difference operator as the indefinite integral relates to the derivative. Thus More explicitly, if , then If F(x) is a solution of this functional equation for a given f(x), then so is F(x)+C(x) for any periodic function C(x) with period 1. Therefore, each indefinite sum actually represents a family of functions. However, due to the Carlson's theorem, the solution equal to its Newton series expansion is unique up to an additive constant C. This unique solution can be represented by formal power series form of the antidifference operator: . (Wikipedia).

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From playlist Continuous Sums: the Definite Integral

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From playlist Continuous Sums: the Definite Integral

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Indefinite Integral of a Vector-Valued Function Example 1

From playlist Calculus

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From playlist Calculus

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From playlist Antiderivatives and the fundamental theorem of calculus | AP Calculus BC | Khan Academy

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From playlist Calculus

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Related pages

Finite difference | List of derivatives and integrals in alternative calculi | Polygamma function | Bernoulli polynomials | Indefinite product | Digamma function | Q-analog | Derivative | Incomplete gamma function | Sinc function | Discrete calculus | Carlson's theorem