List of mathematical identities
Encyclopedia
This page lists identities
in the sense of mathematics
, that is, identically true relations holding in algebra
or between special functions.
Identity (mathematics)
In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...
in the sense of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, that is, identically true relations holding in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
or between special functions.
- Bézout's identityBézout's identityIn number theory, Bézout's identity for two integers a, b is an expressionwhere x and y are integers , such that d is a common divisor of a and b. Bézout's lemma states that such coefficients exist for every pair of nonzero integers...
- Brahmagupta-Fibonacci two-square identityBrahmagupta-Fibonacci identityIn algebra, Brahmagupta's identity, also called Fibonacci's identity, implies that the product of two sums each of two squares is itself a sum of two squares. In other words, the set of all sums of two squares is closed under multiplication...
- Cassini's identity
- Degen's eight-square identityDegen's eight-square identityIn mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which being a sum of eight squares, is itself a sum of eight squares...
- Difference of two squaresDifference of two squaresIn mathematics, the difference of two squares, or the difference of perfect squares, is when a number is squared, or multiplied by itself, and is then subtracted from another squared number...
- Euler's four-square identityEuler's four-square identityIn mathematics, Euler's four-square identity says that the product of two numbers, each of which being a sum of four squares, is itself a sum of four squares. Specifically:=\,...
- Euler's identity
- Fibonacci's identityFibonacci's identityIn mathematics, the term Fibonacci's identity may refer either to* the Brahmagupta–Fibonacci identity in algebra, showing that the set of all sums of two squares is closed under multiplication; or to* the Cassini and Catalan identities on Fibonacci numbers....
- Heine's identity
- Lagrange's identity
- Lagrange's trigonometric identities
- MacWilliams identity
- Parseval's identityParseval's identityIn mathematical analysis, Parseval's identity is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is thePythagorean theorem for inner-product spaces....
- Sun's curious identity
- Vandermonde's identity
Identities for classes of functions
- Logarithmic identitiesLogarithmic identities- Trivial identities :Note that logb is undefined because there is no number x such that bx = 0. In fact, there is a vertical asymptote on the graph of logb at x = 0.- Canceling exponentials :...
- Exponential identities
- Trigonometric identities
- Hyperbolic function identities
- Hypergeometric function identities
- Combinatorial identities
- Summation identities