Difference between revisions of "Reciprocal equation"
From Encyclopedia of Mathematics
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An equation of the form | An equation of the form | ||
| − | $$a_0x^n+a_1x^{n-1}+\ | + | $$a_0x^n+a_1x^{n-1}+\dotsb+a_{n-1}x+a_n=0$$ |
in which the coefficients located at equal distances from the beginning and from the end are equal: $a_i=a_{n-i}$. A reciprocal equation of degree $2n$ may be reduced to an $n$-th degree equation by putting $z=x\pm1/x$. | in which the coefficients located at equal distances from the beginning and from the end are equal: $a_i=a_{n-i}$. A reciprocal equation of degree $2n$ may be reduced to an $n$-th degree equation by putting $z=x\pm1/x$. | ||
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| + | [[Category:Field theory and polynomials]] | ||
Latest revision as of 12:43, 14 February 2020
An equation of the form
$$a_0x^n+a_1x^{n-1}+\dotsb+a_{n-1}x+a_n=0$$
in which the coefficients located at equal distances from the beginning and from the end are equal: $a_i=a_{n-i}$. A reciprocal equation of degree $2n$ may be reduced to an $n$-th degree equation by putting $z=x\pm1/x$.
How to Cite This Entry:
Reciprocal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reciprocal_equation&oldid=34035
Reciprocal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reciprocal_equation&oldid=34035
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article