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Struve's Equation
| Content Provider | Scilit |
|---|---|
| Author | Olver, Frank |
| Copyright Year | 1997 |
| Description | Suppose, for example, that 1, > 0 and 1, < 0. Then we may select ph(1, -1,) = n and ph(1, -1,) = 0. Conditions (14.13) and (14.14) are satisfied with ph 1, = 0 and ph1, = n, and the resulting T is - t n+S ,< phz g +n-6. Alternatively, if we select ph(1, -1,) = - n and ph(1, -1,) = 0, then we would have ph 1, = 0, ph 1, = - n, and T becomes -+n+S ,< ph z ,< tn-6. The solution having the property (14.17) in the phase range [ - tn+ 6, +n-61 is not the same as the solution having this property in [-+n+S, t n -61. Ex. 14.1 When go = 0, show that (14.03) has a formal solution I"+' z b , z - ' in general. When may this construction fail? Ex. 14.2 By transforming to the variable C = 3z3Ia show that the equation daw/dz2 = Z W - Z - ~ has solutions wJ(z), j = 0 , + 1, such that 15.1 The following inhomogeneous form of Bessel's equation has solutions of physical and mathematical interest: Using methods analogous to those of Chapter 5, $4, we readily verify that one solution is Struve's function This series converges for all finite z; indeed z-'-'H,(z) is entire in z. It is also readily established, by uniform convergence, that Hv(z) is entire in v, provided that z#O. Book Name: Asymptotics and Special Functions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47263-4&isbn=9780429064616&doi=10.1201/9781439864548-95&format=pdf |
| Ending Page | 296 |
| Page Count | 5 |
| Starting Page | 292 |
| DOI | 10.1201/9781439864548-95 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1997-01-24 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Asymptotics and Special Functions Mathematical Physics Function Equation Mathematical Converges Readily Struve's Select Ph |
| Content Type | Text |
| Resource Type | Chapter |
