linearly independent solution
1Fluid solution — In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid.In astrophysics, fluid solutions are often… …
2Frobenius solution to the hypergeometric equation — In the following we solve the second order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential… …
3Bessel function — In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel s differential equation: for an arbitrary real or complex number α (the order of the …
4Reduction of order — is a technique in mathematics for solving second order ordinary differential equations. It is employed when one solution y 1(x) is known and a second linearly independent solution y 2(x) is desired.A Simple ExampleConsider the general second… …
5Frobenius method — In mathematics, the Frobenius method, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second order ordinary differential equation of the form in the vicinity of the regular singular point z=0. We can… …
6Bessel-Clifford function — In mathematical analysis, the Bessel Clifford function is an entire function of two complex variables which can be used to provide an alternative development of the theory of Bessel functions. If :pi(x) = frac{1}{Pi(x)} = frac{1}{Gamma(x+1)}is… …
7Overdetermined system — For the philosophical term, see overdetermination. In mathematics, a system of linear equations is considered overdetermined if there are more equations than unknowns.[1] The terminology can be described in terms of the concept of counting… …
8Moore–Penrose pseudoinverse — In mathematics, and in particular linear algebra, a pseudoinverse A+ of a matrix A is a generalization of the inverse matrix.[1] The most widely known type of matrix pseudoinverse is the Moore–Penrose pseudoinverse, which was independently… …
9Linear differential equation — In mathematics, a linear differential equation is a differential equation of the form: Ly = f ,where the differential operator L is a linear operator, y is the unknown function, and the right hand side fnof; is a given function (called the source …
10Theorems and definitions in linear algebra — This article collects the main theorems and definitions in linear algebra. Vector spaces A vector space( or linear space) V over a number field² F consists of a set on which two operations (called addition and scalar multiplication, respectively) …
