| Title:
|
Orthoexponential polynomials and the Legendre polynomials (English) |
| Author:
|
Jaroch, Otakar |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
6 |
| Year:
|
1978 |
| Pages:
|
467-471 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Orthoexponential polynomials can be expressed in terms of the Legendre polynomials. The formulae proved in this paper are useful for the computation of the values of orthoexponential polynomials. It is also possible to re-state, for orthoexponential polynomials, some theorems from the theory of classical orthogonal polynomials. (English) |
| Keyword:
|
orthoexponential polynomials |
| Keyword:
|
Legendre polynomials |
| Keyword:
|
classical orthogonal polynomials |
| MSC:
|
33C45 |
| idZBL:
|
Zbl 0429.33009 |
| idMR:
|
MR0508548 |
| DOI:
|
10.21136/AM.1978.103772 |
| . |
| Date available:
|
2008-05-20T18:10:43Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103772 |
| . |
| Reference:
|
[1] H. Bateman A. Erdélyi: Higher Transcendental Functions, Vol. 2.McGraw-Hill, New York 1953. MR 0058756 |
| Reference:
|
[2] V. Čížek: Methods of Time Domain Synthesis.Research Report Z-44, Czechoslovak Academy of Sciences, Institute of Radioelectronics, Praha, 1960 (in Czech). |
| Reference:
|
[3] R. Courant D. Hilbert: Methoden der mathematischen Physik, Vol. 1.Berlin, 1931 (Russian translation: GITTL, 1951). |
| Reference:
|
[4] A. A. Dmitriyev: Orthogonal Exponential Functions in Hydrometeorology.Gidrometeoizdat, Leningrad, 1973 (in Russian). |
| Reference:
|
[5] O. Jaroch: A Method of Numerical Inversion of Laplace Transforms.Práce ČVUT, Series VI, No. 1, Part I, pp. 332-339. Czech Technical University, Prague 1961 (in Czech). |
| Reference:
|
[6] O. Jaroch: Approximation by Exponential Functions.Aplikace matematiky, Vol. 7, No. 4, pp. 249-264, 1962 (in Czech). Zbl 0112.08003, MR 0158211 |
| Reference:
|
[7] O. Jaroch J. Novotný: Recurrence Relations for Orthogonal Exponential Polynomials and their Derivatives.Acta Polytechnica- Práce ČVUT, Vol. IV (1973), pp. 39-42 (in Czech). |
| Reference:
|
[8] J. H. Laning R. H. Battin: Random Processes in Automatic Control.McGraw-Hill, New York, 1956. MR 0079362 |
| Reference:
|
[9] G. Szegö: Orthogonal Polynomials.American Mathematical Society, New York, 1959. MR 0106295 |
| Reference:
|
[10] D. F. Tuttle: Network Synthesis for Prescribed Transient Response.Massachusetts Institute of Technology, 1949, DSc. Thesis. |
| . |
