This article lists
mathematical identities, that is, ''identically true relations'' holding in
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
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Bézout's identity
In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is the following theorem:
Here the greatest common divisor of and is taken to be . The integers and are called BÃ ...
(despite its usual name, it is not, properly speaking, an identity)
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Binet-cauchy identity
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Binomial inverse theorem
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Binomial identity
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Brahmagupta–Fibonacci two-square identity
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Candido's identity
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Cassini and Catalan identities
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Degen's eight-square identity
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Difference of two squares
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Euler's four-square identity
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Euler's identity
* Fibonacci's identity see
Brahmagupta–Fibonacci identity or
Cassini and Catalan identities
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Heine's identity
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Hermite's identity
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Lagrange's identity
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Lagrange's trigonometric identities
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List of logarithmic identities
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MacWilliams identity
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Matrix determinant lemma
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Newton's identity
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Parseval's identity
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Pfister's sixteen-square identity
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Sherman–Morrison formula
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Sophie Germain identity
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Sun's curious identity
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Sylvester's determinant identity
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Vandermonde's identity
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Woodbury matrix identity
Identities for classes of functions
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Exterior calculus identities
* Fibonacci identities:
Combinatorial Fibonacci identities and
Other Fibonacci identities
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Hypergeometric function identities
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List of integrals of logarithmic functions
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List of topics related to
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List of trigonometric identities
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involvin ...
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Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called ''antitrigonometric'', ''cyclometric'', or ''arcus'' functions) are the inverse functions of the trigonometric functions, under suitably restricted Domain of a functi ...
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Logarithmic identities
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Summation identities
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Vector calculus identities
The following are important identities involving derivatives and integrals in vector calculus.
Operator notation
Gradient
For a function f(x, y, z) in three-dimensional Cartesian coordinate variables, the gradient is the vector field:
:
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See also
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* {{annotated link, List of set identities and relations
External links
A Collection of Algebraic Identities
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Identities