Laguerre polynomials in the inversion of Mellin transform

George J. Tsamasphyros; Pericles S. Theocaris

Aplikace matematiky (1981)

  • Volume: 26, Issue: 3, page 180-193
  • ISSN: 0862-7940

Abstract

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In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function g ( r ) is represented as an expansion of Laguerre polynomials with respect to the variable t = l n r . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last technique is applied to numerical examples.

How to cite

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Tsamasphyros, George J., and Theocaris, Pericles S.. "Laguerre polynomials in the inversion of Mellin transform." Aplikace matematiky 26.3 (1981): 180-193. <http://eudml.org/doc/15194>.

@article{Tsamasphyros1981,
abstract = {In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function $g(r)$ is represented as an expansion of Laguerre polynomials with respect to the variable $t=ln\ r$. The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last technique is applied to numerical examples.},
author = {Tsamasphyros, George J., Theocaris, Pericles S.},
journal = {Aplikace matematiky},
keywords = {Mellin transform; expansion of Laguerre polynomials; numerical inversion; discrete least squares approximation; numerical examples; Mellin transform; expansion of Laguerre polynomials; numerical inversion; discrete least squares approximation; numerical examples},
language = {eng},
number = {3},
pages = {180-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Laguerre polynomials in the inversion of Mellin transform},
url = {http://eudml.org/doc/15194},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Tsamasphyros, George J.
AU - Theocaris, Pericles S.
TI - Laguerre polynomials in the inversion of Mellin transform
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 3
SP - 180
EP - 193
AB - In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function $g(r)$ is represented as an expansion of Laguerre polynomials with respect to the variable $t=ln\ r$. The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last technique is applied to numerical examples.
LA - eng
KW - Mellin transform; expansion of Laguerre polynomials; numerical inversion; discrete least squares approximation; numerical examples; Mellin transform; expansion of Laguerre polynomials; numerical inversion; discrete least squares approximation; numerical examples
UR - http://eudml.org/doc/15194
ER -

References

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  1. I. N. Sneddon, Fourier Transforms, McGraw-Hill, New York, 1951. (1951) Zbl0038.26801MR0041963
  2. D. Bogy, 10.1016/0020-7683(70)90104-6, Int. Journ. Sol. Structures, 6 (1970), 1287-1313. (1970) Zbl0202.25001DOI10.1016/0020-7683(70)90104-6
  3. G. Tsamasphyros, P. S. Theocaris, 10.1007/BF01932274, BIT, 16 (1976), 313-321. (1976) Zbl0336.65059MR0423763DOI10.1007/BF01932274
  4. V. I. Krylov, N. S. Skoblya, Handbook of Numerical Inversion of Laplace Transform, Minsk (1968) and Israel program for scientific translations, Jerusalem, 1969. (1968) Zbl0207.17602MR0391481
  5. F. Tricomi, Transformazione di Laplace e polinomi de Laguerre, R. C. Accad. Naz. Lincei, Cl. Sci. Fis. 1a, 13 (1935), 232-239 and 420-426. (1935) Zbl61.0452.01
  6. G. Doetch, Handbuch der Laplace Transformation, Verlag Birkhäuser, Basel, 1950. (1950) 
  7. A. Papoulis, A New Method of Inversion of the Laplace Transform, Quart. Appl. Math. 14 (1956), 405-414. (1956) Zbl0077.11402MR0082734
  8. W. T. Weeks, 10.1145/321341.321351, Journal ACM. 13 (1966), 419-426. (1966) Zbl0141.33401MR0195241DOI10.1145/321341.321351
  9. R. Piessens, M. Branders, Numerical Inversion of the Laplace Transform Using Generalised Laguerre Polynomials, Proc. IEE 118 (1971), 1517-1522. (1971) MR0323084
  10. R. Piessens, 10.1016/0771-050X(75)90029-7, Jour. Comput. Appl. Mathern. 1 (1975), 115-128, (1975) Zbl0302.65092MR0375743DOI10.1016/0771-050X(75)90029-7
  11. R. Piessens, F. Poleunis, 10.1007/BF01931813, BIT, 11 (1971), 317-327. (1971) Zbl0234.65026MR0288959DOI10.1007/BF01931813
  12. A. Alaylioglu G. Evans, J. Hyslop, Automatic Generation of Quadrature Formulae for Oscillatory Integrals, Соmр. Jour. 18 (1975), 173-176 and 19 (1976), 258-267. (1975) Zbl0301.65009MR0375747
  13. T. Vogel, Les fonctions orthogonales dans les problèmes aux limites de la physique Mathematique, CNRS, 1953. (1953) Zbl0052.29003MR0060053
  14. A. Erdelyi W. Magnus F. Oberthettinger F. G. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, 1954. (1954) 

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