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New Backward Recurrences for Bessel Functions
| Content Provider | Scilit |
|---|---|
| Author | Thacher, Henry C. |
| Copyright Year | 1979 |
| Description | The recurrences for the coefficients of appropriate power series may be used with the Miller algorithm to evaluate , 0,\;\vert x\vert\;{\text{large}})$">, and the modulus and phase of 0,\;\vert x\vert\;{\text{large}})$">. The first converges slightly faster than the power series or the classical recurrence, but requires more arithmetic; the last three give both better ultimate precision and faster convergence than the corresponding asymptotic series. The analysis also leads to a formal continued fraction for the convergence of which increases with . The procedures were tested numerically both for integer and fractional values of v, and for real and complex x. |
| Related Links | https://www.ams.org/mcom/1979-33-146/S0025-5718-1979-0521289-1/S0025-5718-1979-0521289-1.pdf |
| Ending Page | 764 |
| Page Count | 21 |
| Starting Page | 744 |
| ISSN | 00255718 |
| e-ISSN | 10886842 |
| DOI | 10.2307/2006310 |
| Journal | Mathematics of Computation |
| Issue Number | 146 |
| Volume Number | 33 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1979-04-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Bessel Function Power Series Hankel Function Bessel Functions Airy Function Differential Equation Continued Fraction |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Algebra and Number Theory Computational Mathematics |
