Orthoexponential polynomials and the Legendre polynomials

Otakar Jaroch

Aplikace matematiky (1978)

  • Volume: 23, Issue: 6, page 467-471
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Jaroch, Otakar. "Orthoexponential polynomials and the Legendre polynomials." Aplikace matematiky 23.6 (1978): 467-471. <http://eudml.org/doc/15074>.

@article{Jaroch1978,
abstract = {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.},
author = {Jaroch, Otakar},
journal = {Aplikace matematiky},
keywords = {orthoexponential polynomials; Legendre polynomials; classical orthogonal polynomials; orthoexponential polynomials; Legendre polynomials; classical orthogonal polynomials},
language = {eng},
number = {6},
pages = {467-471},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Orthoexponential polynomials and the Legendre polynomials},
url = {http://eudml.org/doc/15074},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Jaroch, Otakar
TI - Orthoexponential polynomials and the Legendre polynomials
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 6
SP - 467
EP - 471
AB - 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.
LA - eng
KW - orthoexponential polynomials; Legendre polynomials; classical orthogonal polynomials; orthoexponential polynomials; Legendre polynomials; classical orthogonal polynomials
UR - http://eudml.org/doc/15074
ER -

References

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  1. H. Bateman A. Erdélyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York 1953. (1953) Zbl0143.29202MR0058756
  2. V. Čížek, Methods of Time Domain Synthesis, Research Report Z-44, Czechoslovak Academy of Sciences, Institute of Radioelectronics, Praha, 1960 (in Czech). (1960) 
  3. R. Courant D. Hilbert, Methoden der mathematischen Physik, Vol. 1, Berlin, 1931 (Russian translation: GITTL, 1951). (1931) Zbl0001.00501
  4. A. A. Dmitriyev, Orthogonal Exponential Functions in Hydrometeorology, Gidrometeoizdat, Leningrad, 1973 (in Russian). (1973) 
  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). (1961) 
  6. O. Jaroch, Approximation by Exponential Functions, Aplikace matematiky, Vol. 7, No. 4, pp. 249-264, 1962 (in Czech). (1962) Zbl0112.08003MR0158211
  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). (1973) 
  8. J. H. Laning R. H. Battin, Random Processes in Automatic Control, McGraw-Hill, New York, 1956. (1956) MR0079362
  9. G. Szegö, Orthogonal Polynomials, American Mathematical Society, New York, 1959. (1959) Zbl0089.27501MR0106295
  10. D. F. Tuttle, Network Synthesis for Prescribed Transient Response, Massachusetts Institute of Technology, 1949, DSc. Thesis. (1949) 

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