Difference between revisions of "Weierstrass elementary factors inequality"
From specialfunctionswiki
| Line 2: | Line 2: | ||
The following formula holds for $|z| \leq 1$: | The following formula holds for $|z| \leq 1$: | ||
$$\left| 1-E_n(z) \right| \leq \left| z \right|^{n+1},$$ | $$\left| 1-E_n(z) \right| \leq \left| z \right|^{n+1},$$ | ||
| − | where $E_n$ denotes a [[Weierstrass elementary factor]]. | + | where $E_n$ denotes a [[Weierstrass elementary factors|Weierstrass elementary factor]]. |
==Proof== | ==Proof== | ||
Latest revision as of 19:11, 26 November 2016
Theorem
The following formula holds for $|z| \leq 1$: $$\left| 1-E_n(z) \right| \leq \left| z \right|^{n+1},$$ where $E_n$ denotes a Weierstrass elementary factor.
