Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Chebyshev_equation> ?p ?o. }
Showing items 1 to 26 of
26
with 100 items per page.
- Chebyshev_equation abstract "Chebyshev's equation is the second order linear differential equation where p is a real constant. The equation is named after Russian mathematician Pafnuty Chebyshev.The solutions are obtained by power series:where the coefficients obey the recurrence relationThese series converge for x in , as may be seen by applyingthe ratio test to the recurrence.The recurrence may be started with arbitrary values of a0 and a1,leading to the two-dimensional space of solutions that arises from second orderdifferential equations. The standard choices are:a0 = 1 ; a1 = 0, leading to the solutionanda0 = 0 ; a1 = 1, leading to the solutionThe general solution is any linear combination of these two.When p is an integer, one or the other of the two functions has its series terminateafter a finite number of terms: F terminates if p is even, and G terminates if p is odd.In this case, that function is a pth degree polynomial (convergingeverywhere, of course), and that polynomial is proportional to the pthChebyshev polynomial.if p is evenif p is oddThis article incorporates material from Chebyshev equation on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.".
- Chebyshev_equation wikiPageID "3760497".
- Chebyshev_equation wikiPageRevisionID "605429716".
- Chebyshev_equation hasPhotoCollection Chebyshev_equation.
- Chebyshev_equation id "3616".
- Chebyshev_equation title "Chebyshev equation".
- Chebyshev_equation subject Category:Ordinary_differential_equations.
- Chebyshev_equation type Abstraction100002137.
- Chebyshev_equation type Communication100033020.
- Chebyshev_equation type DifferentialEquation106670521.
- Chebyshev_equation type Equation106669864.
- Chebyshev_equation type MathematicalStatement106732169.
- Chebyshev_equation type Message106598915.
- Chebyshev_equation type OrdinaryDifferentialEquations.
- Chebyshev_equation type Statement106722453.
- Chebyshev_equation comment "Chebyshev's equation is the second order linear differential equation where p is a real constant.".
- Chebyshev_equation label "Chebyshev equation".
- Chebyshev_equation label "チェビシェフ方程式".
- Chebyshev_equation label "切比雪夫方程".
- Chebyshev_equation sameAs チェビシェフ方程式.
- Chebyshev_equation sameAs m.09zj9j.
- Chebyshev_equation sameAs Q3890369.
- Chebyshev_equation sameAs Q3890369.
- Chebyshev_equation sameAs Chebyshev_equation.
- Chebyshev_equation wasDerivedFrom Chebyshev_equation?oldid=605429716.
- Chebyshev_equation isPrimaryTopicOf Chebyshev_equation.