Difference between revisions of "Chebyshev theorem on the integration of binomial differentials"
From Encyclopedia of Mathematics
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The indefinite integral of the binomial differential | The indefinite integral of the binomial differential | ||
| − | + | $$ | |
| − | + | x^m (a+bx^n)^p | |
| − | + | $$ | |
| − | where | + | where $a$ and $b$ are real numbers and $m$, $n$ and $p$ are rational numbers, cannot be expressed in terms of elementary functions for any $m$, $n$ and $p$, except in the case where (at least) one of $p$, $(m+1)/n$ and $p + (m+1)/n$ is an integer. Obtained by P.L. Chebyshev (1853). |
====Comments==== | ====Comments==== | ||
| − | See also [[ | + | See also [[Differential binomial]]. |
Latest revision as of 21:00, 9 December 2014
The indefinite integral of the binomial differential
$$
x^m (a+bx^n)^p
$$
where $a$ and $b$ are real numbers and $m$, $n$ and $p$ are rational numbers, cannot be expressed in terms of elementary functions for any $m$, $n$ and $p$, except in the case where (at least) one of $p$, $(m+1)/n$ and $p + (m+1)/n$ is an integer. Obtained by P.L. Chebyshev (1853).
Comments
See also Differential binomial.
How to Cite This Entry:
Chebyshev theorem on the integration of binomial differentials. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_theorem_on_the_integration_of_binomial_differentials&oldid=35531
Chebyshev theorem on the integration of binomial differentials. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_theorem_on_the_integration_of_binomial_differentials&oldid=35531
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article