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  2. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    C is used for an arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. Thus, each function has an infinite number of antiderivatives. These formulas only state in another form the assertions in the table of derivatives.

  3. Machin-like formula - Wikipedia

    en.wikipedia.org/wiki/Machin-like_formula

    Machin-like formulas for π can be constructed by finding a set of integers , =, where all the prime factorisations of ⁠ + ⁠, taken together, use a number of distinct primes , and then using either linear algebra or the LLL basis-reduction algorithm to construct linear combinations of arctangents of . For example, in the Størmer formula ...

  4. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    Examples of proper fractions are 2/3, –3/4, and 4/9; examples of improper fractions are 9/4, –4/3, and 3/3. improper integral In mathematical analysis , an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number , ∞ {\displaystyle \infty } , − ∞ ...

  5. Simpson's rule - Wikipedia

    en.wikipedia.org/wiki/Simpson's_rule

    "Simpson's Rule Cumulative Integration with MS Excel and Irregularly-spaced Data" (PDF). Journal of Mathematical Sciences and Mathematics Education. 12 (2): 19; Kalambet, Yuri; Kozmin, Yuri; Samokhin, Andrey (2018). "Comparison of integration rules in the case of very narrow chromatographic peaks".

  6. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    2.1.4 Scalar curvature. ... Download as PDF; Printable version ... The variation formula computations above define the principal symbol of the mapping which sends a ...

  7. List of equations in classical mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in...

    Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...

  8. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...

  9. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

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