Large parameter cases of the Gauss hypergeometric function
We consider the asymptotic behavior of the Gauss hypergeometric function when several of the parameters a,b,c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and which cases need more atte...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2003-04, Vol.153 (1-2), p.441-462 |
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| container_issue | 1-2 |
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| container_title | Journal of computational and applied mathematics |
| container_volume | 153 |
| creator | Temme, Nico M |
| description | We consider the asymptotic behavior of the Gauss hypergeometric function when several of the parameters a,b,c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2 functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available. |
| doi_str_mv | 10.1016/S0377-0427(02)00627-1 |
| format | Article |
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| ispartof | Journal of computational and applied mathematics, 2003-04, Vol.153 (1-2), p.441-462 |
| issn | 0377-0427 1879-1778 |
| language | eng |
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| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Approximations and expansions Asymptotic expansion Exact sciences and technology Functions of a complex variable Gauss hypergeometric function Mathematical analysis Mathematics Sciences and techniques of general use Special functions |
| title | Large parameter cases of the Gauss hypergeometric function |
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