Difference between revisions of "Gauss-Lucas theorem"
From Encyclopedia of Mathematics
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''Gauss theorem'' | ''Gauss theorem'' | ||
| − | Let | + | Let $f(z)$ be a complex polynomial, i.e., $f(z)\in\mathbf C[z]$. Then the zeros of the derivative $f'(z)$ are inside the convex polygon spanned by the zeros of $f(z)$. |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Hille, "Analytic function theory" , '''1''' , Chelsea, reprint (1982) pp. 84</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> P. Henrici, "Applied and computational complex analysis" , '''I''' , Wiley, reprint (1988) pp. 463ff</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> B.J. Lewin, "Nullstellenverteilung ganzer Funktionen" , Akademie Verlag (1962) pp. 355</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Hille, "Analytic function theory" , '''1''' , Chelsea, reprint (1982) pp. 84</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> P. Henrici, "Applied and computational complex analysis" , '''I''' , Wiley, reprint (1988) pp. 463ff</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> B.J. Lewin, "Nullstellenverteilung ganzer Funktionen" , Akademie Verlag (1962) pp. 355</TD></TR></table> | ||
Latest revision as of 17:21, 28 October 2014
Gauss theorem
Let $f(z)$ be a complex polynomial, i.e., $f(z)\in\mathbf C[z]$. Then the zeros of the derivative $f'(z)$ are inside the convex polygon spanned by the zeros of $f(z)$.
References
| [a1] | E. Hille, "Analytic function theory" , 1 , Chelsea, reprint (1982) pp. 84 |
| [a2] | P. Henrici, "Applied and computational complex analysis" , I , Wiley, reprint (1988) pp. 463ff |
| [a3] | B.J. Lewin, "Nullstellenverteilung ganzer Funktionen" , Akademie Verlag (1962) pp. 355 |
How to Cite This Entry:
Gauss-Lucas theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gauss-Lucas_theorem&oldid=16185
Gauss-Lucas theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gauss-Lucas_theorem&oldid=16185
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article