Previous |  Up |  Next

Article

Title: Laguerre polynomials in the inversion of Mellin transform (English)
Author: Tsamasphyros, George J.
Author: Theocaris, Pericles S.
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 26
Issue: 3
Year: 1981
Pages: 180-193
Summary lang: English
Summary lang: Czech
.
Category: math
.
Summary: 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. (English)
Keyword: Mellin transform
Keyword: expansion of Laguerre polynomials
Keyword: numerical inversion
Keyword: discrete least squares approximation
Keyword: numerical examples
MSC: 44A10
MSC: 44A15
MSC: 65R10
MSC: 65T05
idZBL: Zbl 0464.65089
idMR: MR0615605
.
Date available: 2008-05-20T18:16:52Z
Last updated: 2015-07-09
Stable URL: http://hdl.handle.net/10338.dmlcz/103910
.
Reference: [1] I. N. Sneddon: Fourier Transforms.McGraw-Hill, New York, 1951. MR 0041963
Reference: [2] D. Bogy: On the Problem of Edge-Bonded Elastic Quarter-Planes Loaded at the Boundary.Int. Journ. Sol. Structures, 6 (1970), 1287-1313. Zbl 0202.25001, 10.1016/0020-7683(70)90104-6
Reference: [3] G. Tsamasphyros, P. S. Theocaris: Numerical Inversion of Mellin Transforms.BIT, 16 (1976), 313-321. Zbl 0336.65059, MR 0423763, 10.1007/BF01932274
Reference: [4] V. I. Krylov, N. S. Skoblya: Handbook of Numerical Inversion of Laplace Transform.Minsk (1968) and Israel program for scientific translations, Jerusalem, 1969. MR 0391481
Reference: [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.
Reference: [6] G. Doetch: Handbuch der Laplace Transformation.Verlag Birkhäuser, Basel, 1950.
Reference: [7] A. Papoulis: A New Method of Inversion of the Laplace Transform.Quart. Appl. Math. 14 (1956), 405-414. MR 0082734
Reference: [8] W. T. Weeks: Numerical Inversion of Laplace Transforms Using Laguerre Functions.Journal ACM. 13 (1966), 419-426. Zbl 0141.33401, MR 0195241, 10.1145/321341.321351
Reference: [9] R. Piessens, M. Branders: Numerical Inversion of the Laplace Transform Using Generalised Laguerre Polynomials.Proc. IEE 118 (1971), 1517-1522. MR 0323084
Reference: [10] R. Piessens: A Bibliography on Numerical Inversion of the Laplace Transform and Applications.Jour. Comput. Appl. Mathern. 1 (1975), 115-128, Zbl 0302.65092, MR 0375743, 10.1016/0771-050X(75)90029-7
Reference: [11] R. Piessens, F. Poleunis: A Numerical Method for the Integration of Oscillatory Functions.BIT, 11 (1971), 317-327. Zbl 0234.65026, MR 0288959, 10.1007/BF01931813
Reference: [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. MR 0375747
Reference: [13] T. Vogel: Les fonctions orthogonales dans les problèmes aux limites de la physique Mathematique.CNRS, 1953. Zbl 0052.29003, MR 0060053
Reference: [14] A. Erdelyi W. Magnus F. Oberthettinger F. G. Tricomi: Tables of Integral Transforms.McGraw-Hill, New York, 1954.
.

Files

Files Size Format View
AplMat_26-1981-3_4.pdf 1.994Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo