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  2. Nonelementary integral - Wikipedia

    en.wikipedia.org/wiki/Nonelementary_Integral

    Nonelementary integral. In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field ...

  3. Liouville's theorem (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Liouville's_theorem...

    In mathematics, Liouville's theorem, originally formulated by French mathematician Joseph Liouville in 1833 to 1841, [1] [2] [3] places an important restriction on antiderivatives that can be expressed as elementary functions . The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions.

  4. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    Calculus. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f.

  5. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...

  6. Product integral - Wikipedia

    en.wikipedia.org/wiki/Product_integral

    The product integral also occurs in control theory, as the Peano–Baker series describing state transitions in linear systems written in a master equation type form. General (non-commutative) case. The Volterra product integral is most useful when applied to matrix-valued functions or functions with values in a Banach algebra.

  7. 1/4 + 1/16 + 1/64 + 1/256 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B...

    1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = 3 4. In mathematics, the infinite series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series with first term 1 4 and common ratio 1 4 ...

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