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  2. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is,

  3. List of open-source software for mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_open-source...

    The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.

  4. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    (), where (2n − 1)!! is the double factorial of (2n − 1), which is the product of all odd numbers up to (2n − 1). This series diverges for every finite x , and its meaning as asymptotic expansion is that for any integer N ≥ 1 one has erfc ⁡ x = e − x 2 x π ∑ n = 0 N − 1 ( − 1 ) n ( 2 n − 1 ) ! !

  5. List of computer algebra systems - Wikipedia

    en.wikipedia.org/wiki/List_of_computer_algebra...

    The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.

  6. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms can be used to solve any equation of continuous functions. However, most root-finding algorithms do not guarantee that they will find all roots of a function, and if such an algorithm does not find any root, that ...

  7. Tupper's self-referential formula - Wikipedia

    en.wikipedia.org/wiki/Tupper's_self-referential...

    The formula was defined by Jeff Tupper and appears as an example in his 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms. [1] This paper discusses methods related to the GrafEq formula-graphing program developed by Tupper. [2]

  8. Yates analysis - Wikipedia

    en.wikipedia.org/wiki/Yates_Analysis

    A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article. Formalized by Frank Yates , a Yates analysis exploits the special structure of these designs to generate least squares estimates for factor effects for ...

  9. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: =. That difference is algebraically factorable as (+) (); if neither factor equals one, it is a proper factorization of N.