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- Liouville's_formula abstract "In mathematics, Liouville's formula, also known as the Abel-Jacobi-Liouville Identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system. The formula is named after the French mathematician Joseph Liouville. Jacobi's formula provides another representation of the same mathematical relationship.Liouville's formula is a generalization of Abel's identity and can be used to prove it. Since Liouville's formula relates the different linearly independent solutions of the system of differential equations, it can help to find one solution from the other(s), see the example application below.".
- Liouville's_formula wikiPageExternalLink book-ode.
- Liouville's_formula wikiPageID "16199733".
- Liouville's_formula wikiPageRevisionID "543366906".
- Liouville's_formula hasPhotoCollection Liouville's_formula.
- Liouville's_formula subject Category:Articles_containing_proofs.
- Liouville's_formula subject Category:Mathematical_identities.
- Liouville's_formula subject Category:Ordinary_differential_equations.
- Liouville's_formula type Abstraction100002137.
- Liouville's_formula type Attribute100024264.
- Liouville's_formula type Communication100033020.
- Liouville's_formula type DifferentialEquation106670521.
- Liouville's_formula type Equation106669864.
- Liouville's_formula type Identity104618070.
- Liouville's_formula type MathematicalIdentities.
- Liouville's_formula type MathematicalStatement106732169.
- Liouville's_formula type Message106598915.
- Liouville's_formula type OrdinaryDifferentialEquations.
- Liouville's_formula type Personality104617562.
- Liouville's_formula type Statement106722453.
- Liouville's_formula comment "In mathematics, Liouville's formula, also known as the Abel-Jacobi-Liouville Identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system. The formula is named after the French mathematician Joseph Liouville.".
- Liouville's_formula label "Liouville's formula".
- Liouville's_formula label "Liouvillesche Formel".
- Liouville's_formula label "Формула Лиувилля — Остроградского".
- Liouville's_formula sameAs Liouvillesche_Formel.
- Liouville's_formula sameAs m.064rb7v.
- Liouville's_formula sameAs Q1827325.
- Liouville's_formula sameAs Q1827325.
- Liouville's_formula sameAs Liouville's_formula.
- Liouville's_formula wasDerivedFrom Liouville's_formula?oldid=543366906.
- Liouville's_formula isPrimaryTopicOf Liouville's_formula.