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In mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act. They are named after the mathematician George Green , who discovered Green's theorem .
In his paper "The S-Matrix in Quantum electrodynamics", [1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach.
This category is for mathematical identities, i.e. identically true relations holding in some area of algebra (including abstract algebra, or formal power series). Subcategories This category has only the following subcategory.
Using the Green's function for the three-variable Laplace operator, one can integrate the Poisson equation in order to determine the potential function. Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
WASHINGTON (Reuters) -The FBI has been investigating a longtime Exxon Mobil consultant over the contractor's alleged role in a hack-and-leak operation that targeted hundreds of the oil company’s ...
Roope Hintz had his first two-goal game of the season and Jake Oettinger stopped 25 shots as the Dallas Stars beat the surging Washington Capitals 3-1 on Monday night. Rookie defenseman Lian ...
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.