| Title:
|
Asymptotic ratios of Bessel functions of purely imaginary argument (English) |
| Author:
|
Trlifaj, Ladislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
1 |
| Year:
|
1974 |
| Pages:
|
1-6 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Riccati equations as well as some interesting inequalities for the ratios of Bessel functions of purely imaginary argument $T_p(x;1)=\frac {K_p(x)}{xK_{p+1}(x)}$ and $T_p(x;-1)=\frac {I_p(x)}{xI_{p-1}(x)}$ are derived. Solutions of the Riccati equations are given in terms of power series in $p^{-1}$. In particular, the asymptotic formulae for $T_p(x;\pm 1)$ with a remainder of order $O(p^{-5})$ are obtained. For $p$ small, they represent an asymptotic expansion in $x$ up to the order $O(x^{-5})$. () |
| MSC:
|
33A40 |
| MSC:
|
33C10 |
| idZBL:
|
Zbl 0278.33015 |
| idMR:
|
MR0340669 |
| DOI:
|
10.21136/AM.1974.103508 |
| . |
| Date available:
|
2008-05-20T17:57:54Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103508 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Calogero F., al.: .Nuovo Cimento 67 A (1970), 641 - 657. Zbl 0195.11801 |
| Reference:
|
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| Reference:
|
[7] Watson G. N.: Theory of Bessel functions.Cambridge University Press; Cambridge (1962). |
| Reference:
|
[8] Montroll E. W.: .J. Math, and Physics 25 (1946), 37-48. Zbl 0063.04081, MR 0016499 |
| Reference:
|
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| Reference:
|
[10] Olver F. W. J.: Bessel functions, part III.Royal Soc. Math. Tables, vol. 7, University Press; Cambridge (1960). Zbl 0094.31603, MR 0119441 |
| Reference:
|
[11] Gray A., Mathews G. B. A.: A treatise on Bessel functions and their application to physics.second edition (russian translation), Izdateľstvo inostrannoy literatury; Moscow (1953). |
| . |
