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Nicholson's Integral for J2v (z) + Y2v (z)
| Content Provider | Scilit |
|---|---|
| Author | Olver, Frank |
| Copyright Year | 1997 |
| Description | Finally, we displace the paths for the inner integrals into the lines Imo = +n and Im o = -4n, respectively, and then refer to equation (8.03) of Chapter 7. Thus we arrive at Nicholson's integral: 8 Nv (r ) Po (2z sinh w) cosh (2vw) dw. (7.01) Although the foregoing derivation can be placed on a sound footing, the analysis is difficult.' Instead, following Wilkins (1948) we shall verify the suggested result by quite a different method. 7.2 Theorem 7.1 The integral (7.0 1 ) converges when I ph zl< +n and equals J,? ( z ) + Y,? ( z ) . Book Name: Asymptotics and Special Functions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47263-4&isbn=9780429064616&doi=10.1201/9781439864548-113&format=pdf |
| Ending Page | 359 |
| Page Count | 2 |
| Starting Page | 358 |
| DOI | 10.1201/9781439864548-113 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1997-01-24 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Asymptotics and Special Functions Converges |
| Content Type | Text |
| Resource Type | Chapter |
