In biochemistry, the σ factor (or specificity factor) is a protein found in RNA polymerase. In biology, the sigma receptor (σ–receptors) is a type of cell surface receptor. Theoretical spectral analysis uses σ as standard deviation opposed to lowercase mu as the absolute mean value.
In statistics (as mentioned above), σ represents the standard deviation of a population or probability distribution. In probability theory and statistics, Σ denotes the covariance matrix of a set of random variables, to distinguish it from the summation operator. In complex analysis, σ is used in the Weierstrass sigma-function. In applied mathematics, σ(T) denotes the spectrum of a linear map T. In number theory, σ is included in various divisor functions, especially the sigma function or sum-of-divisors function. Σ(A), denoting the generated sigma-algebra of a set A Sigma algebra also includes terms such as: In mathematical analysis and in probability theory, there is a type of algebra of sets known as σ-algebra (aka σ-field). In topology, σ-compact topological space is one that can be written as a countable union of compact subsets. In statistics, σ represents standard deviation of population or probability distribution (as opposed to lowercase mu or μ, used for mean). In general mathematics, lowercase σ is commonly used to represent unknown angles, as well as serving as a shorthand for "countably", whereas Σ is regularly used as the operator for summation, e.g.:
In linguistics, Σ represents the set of symbols that form an alphabet (see also computer science). In phonology, σ is used to represent syllables. The uppercase form of sigma (Σ) was re-borrowed into the Latin alphabet-more precisely, the International African Alphabet-to serve as the uppercase of modern esh (lowercase: ʃ). In Modern Greek, this sound is voiced to /z/ before /m/, /n/, /v/, /ð/ or /ɣ/. In both Ancient and Modern Greek, the sigma represents the voiceless alveolar fricative /s/. The lowercase (σ) & uppercase (Σ) sigma are used for:
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