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- Hadamard_regularization abstract "In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part, introduced by Hadamard (1923, book III, chapter I, 1932). Riesz (1938, 1949) showed that this can be interpreted as taking the meromorphic continuation of a convergent integral.If the Cauchy principal value integral exists, then it may be differentiated with respect to x to obtain the Hadamard finite part integral Note that the symbols and are used here to denote Cauchy principal value and Hadamard finite-part integrals respectively. The Hadamard finite part integral above (for a<x<b) may also be given by the following equivalent definitions: The definitions above may be derived by assuming that the function f(t) is differentiable infinitely many times at t=x for a<x<b, that is, by assuming that f(t) can be represented by its Taylor series about t=x. For details, see Ang (2013).Integral equations containing Hadamard finite part integrals (with f(t) unknown) are termed hypersingular integral equations. Hypersingular integral equations arise in the formulation of many problems in mechanics, such as in fracture analysis.".
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- Hadamard_regularization wikiPageID "15866439".
- Hadamard_regularization wikiPageRevisionID "606321815".
- Hadamard_regularization authorlink "Jacques Hadamard".
- Hadamard_regularization hasPhotoCollection Hadamard_regularization.
- Hadamard_regularization last "Hadamard".
- Hadamard_regularization loc "book III, chapter I".
- Hadamard_regularization year "1923".
- Hadamard_regularization year "1932".
- Hadamard_regularization subject Category:Integrals.
- Hadamard_regularization subject Category:Summability_methods.
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- Hadamard_regularization type Integral106015505.
- Hadamard_regularization type Integrals.
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- Hadamard_regularization comment "In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part, introduced by Hadamard (1923, book III, chapter I, 1932).".
- Hadamard_regularization label "Hadamard regularization".
- Hadamard_regularization label "Regularización de Hadamard".
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