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Asymptotic Properties for Complex Variables
| Content Provider | Scilit |
|---|---|
| Author | Olver, Frank |
| Copyright Year | 1997 |
| Description | Although the choice of the negative real axis as boundary for A simplified the narrative in this example, it restricted the regions K,(a,) (and their z maps) unnecessarily. When a , = - co +is, the region K,(a,) can be extended by rotating the cut in the positive sense until it coincides with the positive imaginary axis. The total region of validity is then -fn < ph < < jn. Further extension is precluded by the monotonicity condition. Similarly when a , = -co-is the maximal K,(a,) is - j n < p h < < f n . Ex. 11.1 Let € = + 1 be the only finite singularities of $(a, and Y ( F ) converge at infinity. Using all necessary Riemann sheets sketch the maximal region KI(-a) . Ex. 11.2 Let aJ be at infinity and Conditions (i) and (ii) of $1 1.3 be replaced by the stronger conditions: (i) the € map of gJ is a polygonal arc; (ii) as t passes along gJ from a) to I, Re(€(t)) is strictly increasing if j = 1 or strictly decreasing if j = 2. Show that HJ(aJ) is a domain. Book Name: Asymptotics and Special Functions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47263-4&isbn=9780429064616&doi=10.1201/9781439864548-79&format=pdf |
| Ending Page | 241 |
| Page Count | 1 |
| Starting Page | 241 |
| DOI | 10.1201/9781439864548-79 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1997-01-24 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Asymptotics and Special Functions Mathematical Physics |
| Content Type | Text |
| Resource Type | Chapter |
