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This is a list of open-source software to be used for high-order mathematical calculations. This software has played an important role in the field of mathematics. [1] Open-source software in mathematics has become pivotal in education because of the high cost of textbooks. [2]
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This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
Mathematical notation uses a symbol that compactly represents summation of many similar terms: the summation symbol, , an enlarged form of the upright capital Greek letter sigma. This is defined as = a i = a m + a m + 1 + a m + 2 + ... + a n - 1 + a n
In mathematics, by sigma function one can mean one of the following: The sum-of-divisors function σ a ( n ), an arithmetic function Weierstrass sigma function , related to elliptic functions
Sigma algebra also includes terms such as: σ(A), denoting the generated sigma-algebra of a set A; Σ-finite measure (see measure theory) In number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function. In applied mathematics, σ(T) denotes the spectrum of a linear map T.
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field, where the σ comes from the German "Summe" [1]) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair (,) is called a measurable space.