| Title:
|
Elementary evaluation of Fresnel's integrals (English) |
| Author:
|
Výborný, Rudolf |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
401-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We evaluate the Fresnel integrals by using the Leibniz rule only on a finite interval. (English) |
| Keyword:
|
evaluation |
| Keyword:
|
Fresnel integrals |
| Keyword:
|
Leibniz rule |
| MSC:
|
26A06 |
| MSC:
|
26A09 |
| idZBL:
|
Zbl 0739.26001 |
| idMR:
|
MR1146399 |
| DOI:
|
10.21136/MB.1991.126022 |
| . |
| Date available:
|
2009-09-24T20:47:59Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126022 |
| . |
| Reference:
|
[FL] H. Flanders: On the Fresnel integrals.Amer. Math. Monthly 89 (1982), 264-266. Zbl 0599.26012, MR 0650673, 10.1080/00029890.1982.11995429 |
| Reference:
|
[JA] V. Jarník: Integrální počet II.ČSAV, Praha, 1955, pp. 340-342 and 361-363. |
| Reference:
|
[Mac] E. J. McShane: Unified integration.Academic Press, Inc., Orlando, 1983. Zbl 0551.28001, MR 0740710 |
| Reference:
|
[ML] R. M. McLeod: The generalized Riemann integral.The Mathematical Association of America, Washington DC, 1980. Zbl 0486.26005, MR 0588510 |
| Reference:
|
[SW] J. D. DePree, Ch. W. Swartz: Introduction to Real Analysis.John Wiley & Sons, New York, 1988, p. 199. MR 1042294 |
| Reference:
|
[WE] R. Weinstock: Elementary Evaluations of $\int_0^{infty} e^{-x^2} dx$, $\int_0^{infty} \cos x^2 dx$, and $\int_0^{infty} \sin x^2 dx$.Amer. Math. Monthly 97 (1990), 39-42. MR 1034348 |
| Reference:
|
[YZ] J. van Yzeren: Moivre's and Fresnel's integrals by simple integration.Amer. Math. Monthly 86 (1979), 691-693. Zbl 0446.26003, MR 1539141 |
| . |
