# Differential binomial

From Encyclopedia of Mathematics

An expression of the type

where and are real numbers, while , and are rational numbers. The indefinite integral of a differential binomial,

is reduced to an integral of rational functions if at least one of the numbers , and is an integer. In all other cases, the integral of a differential binomial cannot be expressed by elementary functions (P.L. Chebyshev, 1853).

#### Comments

The statement on the reduction to an integral of rational functions is called the Chebyshev theorem on the integration of binomial differentials.

**How to Cite This Entry:**

Differential binomial. L.D. Kudryavtsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Differential_binomial&oldid=11396

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098