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The Hypergeometric Function
| Content Provider | Scilit |
|---|---|
| Author | Olver, Frank |
| Copyright Year | 1997 |
| Description | For the principal branch with 121 < 1 this result is verifiable from the definition (9.03): the M-test shows that this series converges uniformly in any bounded region of the complex a, b, c space. The extension to lzl2 1 and other branches is immediately achieved by means of Theorem 3.2; any point within the unit disk, other than the origin, may be taken as z0 in Condition (iv) of this theorem. The points z = 0, 1, and a are excluded in the statement of the final result, because F(a, b; c; z) may not exist there.' 9.3 Many well-known functions are expressible in the notation of the hypergeometric function. For example, the principal branch of (1 -2)-" is also the principal branch of F(a, 1 ; 1 ;z). Other examples are stated in Exercises 9.1, 9.2, and 10.1 below. Book Name: Asymptotics and Special Functions |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47263-4&isbn=9780429064616&doi=10.1201/9781439864548-61&format=pdf |
| Ending Page | 180 |
| Page Count | 4 |
| Starting Page | 177 |
| DOI | 10.1201/9781439864548-61 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1997-01-24 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Asymptotics and Special Functions Hypergeometric Function Principal Branch |
| Content Type | Text |
| Resource Type | Chapter |
