Chebyshev's equation is the second order linear differential equation In mathematics, and particularly in analysis, an ordinary differential equation (or ODE) is an equation that involves the derivatives of an unknown function of one variable. ...
where P is a real constant. The equation is named after Russian mathematician Pafnuty Chebyshev. Pafnuty Lvovich Chebyshev Pafnuty Lvovich Chebyshev (ПафнуÌтий ЛьвоÌвич Чебышёв) (May 16, 1821 - December 9, 1894) was a Russian mathematician. ...
There are two independent solutions which are given as series by:
and
In each case, the coefficients are given by the recursion
This article incorporates material from Chebyshev equation on PlanetMath, which is licensed under the GFDL. PlanetMath is a free, collaborative, online mathematics encyclopedia. ...
In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power.
Every cubic equation with real coefficients has at least one solution x among the real numbers; this is a consequence of the intermediate value theorem.
Therefore the Chebyshev cube root is in fact an analytic function on the whole of the domain D. An alternative construction of the Chebyshev cube root in terms of hypergeometric functions is sketched in the next subsection.
Chebyshev always acknowledged the great influence Brashman had been on him while studying at university, and credited him as the main influence in directing his research interests, referring to their "precious personal talks".
Chebyshev submitted a paper on The calculation of roots of equations in which he solved the equation y = f(x) by using a series expansion for the inverse function of f.
Chebyshev continued to aim at international recognition with his second paper, written again in French, appearing in 1844 published by Crelle in his journal.
Feeds |
Contact