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The mean value theorem and analytic functions
| Content Provider | Scilit |
|---|---|
| Author | Johnston, Elgin H. |
| Copyright Year | 1983 |
| Description | It is well known that the mean value theorem (MVT) does not, in general, hold for analytic functions. The most familiar example to this effect is f(z) = $e_{z}$ since $e^{2πi}−e^{0}≠2πie^{z0}$ for any $z_{0}$∈ℂ. On the other hand, it is easy to show that the MVT holds in ℂ if f(z) is a polynomial of degree at most 2. Thus it is natural to ask what conditions on a function f(z) analytic in a domain D are necessary and sufficient for f(z) to satisfy the MVT in D. This is one of the questions answered in this paper. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A86A9079D8044166F3CDB551D1B8C055/S001309150000434Xa.pdf/div-class-title-the-mean-value-theorem-and-analytic-functions-div.pdf |
| Ending Page | 295 |
| Page Count | 7 |
| Starting Page | 289 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s001309150000434x |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 3 |
| Volume Number | 26 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1983-10-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Mean Value Analytic Functions Value Theorem Mvt Holds Questions Answered 2πie Z0 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
