Chebyshev theorem on the integration of binomial differentials

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The indefinite integral of the binomial differential

where and are real numbers and and are rational numbers, cannot be expressed in terms of elementary functions for any and , except in the case where (at least) one of and is an integer. Obtained by P.L. Chebyshev (1853).


See also Differential binomial.

How to Cite This Entry:
Chebyshev theorem on the integration of binomial differentials. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article