1. Foundating papers

[ 1 ] 1935. Widder D.V. "An application of Laguerre polynomials", Duke Math. J. 1:126-136.

[ 2 ] 1966. Weeks W.T. "Numerical inversion of Laplace transforms using Laguerre functions", J. ACM. 13(3):419-426.

[ 3 ] 1955. Salzer H.E. "Orthogonal Polynomials Arising in the Numerical Evaluation of Inverse Laplace Transforms", Math. Comput., 9(52):164-177.

[ 4 ] 1971. Piessens, R. "Gaussian quadrature formulas for the numerical integration of Bromwich's integral and the inversion of the Laplace transform". J. Engineer. Math. 5(1):1-9.

[ 5 ] 1966. Gaver D.P.Jr. "Observing stochastic processes and approximate transform inversion", Operational Res. 14(3):444459.

[ 6 ] 1970. Stehfest H. "Algorithm 368 [D5] : Numerical inversion of Laplace transforms", Comm. ACM 13(1):47-49 and 13(10):624.

[ 7 ] 1968. Dubner H. and J. Abate. "Numerical inversion of Laplace transforms by relating them to finite Fourier-cosine transform", J. ACM 15(1):115-123.

[ 8 ] 1970. Cooley J.W., P.A.W. Lewis and P.D. Welch. "The FFT (fast Fourier transform) algorithm : programming considerations in the calculation of sine, cosine and Laplace transforms", J. Sound Vib. 12(3):315-337.

[ 9 ] 1954. Kautz W.H. "Transient Synthesis in the Time Domain", IRE Trans. Circuit Theory, CT1(Sept.):2939.

a) Articles de synthèse

[ 10 ] 1975. Piessens R. "A bibliography on numerical inversion of the Laplace transform and applications. And a supplement". J. Comp. Appl. Math. 1(2):115-126. and 2(3):225-228.

[ 11 ] 1979. Davies B. and Martin B."Numerical inversion of Laplace transforms: a survey and comparision of methods," J. Comp. Phys, 33:1-32

[ 12 ] 1994. Cheng, A.H-D., P. Sidaurik and Y. Abousleiman. "Approximate inversion of the Laplace transform", The Mathematica Journal 4(2):7682.

2. Papers

[ 13 ] 1936. Bateman H. "Two systems of polynomials for the solution of Laplace's integral equation", Duke Math. J. 2:569-577.

[ 14 ] 1966. Berger B.S. "Inversion of the N-dimensional Laplace transform", Math. Comp. 20(95):418-421.

[ 15 ] 1968. Berger B.S. "The inversion of the Laplace transform with applications to the vibrations of continuous elastic bodies", J. Appl. Mech. 35:837-839.

[ 16 ] 1973. Berger B.S. and Duangudom S. "A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications", J. Appl. Mech. (Transactions of the ASME) 40:1110-1112.

[ 17 ] 1940. Boas R.P. and D.V. Widder. "An inversion formula for the Laplace integral", Duke Math. J. 6:126.

[ 18 ] 1993. Cipra B. "The FFT : making technology fly", SIAM News 26(3), 4 pages (www.siam.org/siamnews/mtc/mtc593.htm).

[ 19 ] 1965. Cooley J.W. and J.W. Tukey. "An algorithm for the machine calculation of complex Fourier series", Math. Comp. 19(90):297-301.

[ 20 ] 1990. Cope D.K. "Convergence of Piessens' method for numerical inversion of the Laplace transform on the real line", Siam J. Numer. Anal., 27(5):13451354.

[ 21 ] 1976. Crump K.S. "Numerical inversion of Laplace transforms using a Fourier series approximation", J. ACM 23(1):89-96.

[ 22 ] 1966. DeBalbine G. and J. Franklin. "The calculation of Fourier integrals", Math. Comp. 20(96):570-589.

[ 23 ] 1992. Dubner H. "Partitions approximated by finite cosine-series", Math. Comput. 58(198):729736.

[ 24 ] 1974. Durbin F. "Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method", Computer J. 17:371-376.

[ 25 ] 1948. Elmore W.C. "The transient response of damped linear networks", J. Appl. Phys. 19(1):5563

[ 26 ] 1988. Garbow B.S., Giunta G., Lyness J. N. and A. Murli. "Software for the implementation of Weeks's method for the inverse Laplace transform problem", ACM Trans. Math. Soft. 14(2):163-170.

[ 27 ] 1986. Helstrom C.W. "Calculating error probabilities for intersymbol and cochanel interference", IEEE Trans. Commun., Com34(5):430435.

[ 28 ] 1954. Hli F. B. "A general method for time domain network synthesis", IRE Trans. Circuit Theory, CT1(Sept.):2128.

[ 29 ] 1956. Hurwitz H.Jr. and P.F. Zweifel. "Numerical quadrature of Fourier transform integrals.", Math. Comput., 10(55):140-149.

[ 30 ] 1971. Longman I.M. "Computation of the Padé table", Intern. J. Comput. Math. B 3:53-64.

[ 31 ] 1972. Longman I.M. "Numerical Laplace transform inversion of a function arising in viscoelasticity", J. Comput. Phys. 10:224231.

[ 32 ] 1973. Longman I.M. "On the generation of rational function approximation for Laplace transform inversion with application to viscoelasticity", SIAM J. Appl. Math. 24(4):429440

[ 33 ] 1975. Longman I.M. "Application of best rational function approximation for Laplace transform inversion", J. Comp. Appl. Math. 1(1):1723.

[ 34 ] 1964. MacDonald J.R. "Accelerated convergence, divergence, iteration, extrapolation, and curve fitting", J. Appl. Phys. 35(10):3034-3041.

[ 35 ] 1966. Miller M.K. and W. T. Guy Jr. "Numerical inversion of the Laplace transform by use of Jacobi polynomials", SIAM J. Numer. Anal. 3(4):624-635.

[ 36 ] 1972. Nance R.E., U.N. Bath and B.G. Claybrook. "Busy period analysis of a time-sharing system : transform Inversion", J. ACM, 19(3):453463.

[ 37 ] 1961. Norden H. V. "Numerical inversion of the Laplace transform", Acta Acad. Aboensis, Ser. B, 22:3-50.

[ 38 ] 1990. Obi W.C. "Error analysis of a Laplace transform analysis", Siam J. Numer. Anal., 27(2):457469.

[ 39 ] 1955. Papoulis A. "On the expansion of a network response into a series of orthogonal functions", IRE Trans. Circuit Theory, CT2(Sept.):283.

[ 40 ] 1957. Papoulis A. "A new method of inversion oÍ the Laplace transform", Quart. Appl. Math. 14(4):405-414.

[ 41 ] 1969. Piessens R. "Numerical inversion of the Laplace transform", IEEE Trans. Automatic Control AC-14:299-301.

[ 42 ] 1973. Piessens R. "Gaussian quadrature formulas for Bromwich's integral". Comm. ACM 16(8):486-487.

[ 43 ] 1989. Ryabov V.M. "The properties of quadrature formulas of the highest accuracy used for Laplace Transform inversion", URSS Comput. Maths. Math.Phys, 29(4):8386.

[ 44 ] 1960. Schmittroth L.A. "Numerical inversion of Laplace transforms", Comm. ACM 3:171-173.

[ 45 ] 1989. Schreiber F. "Effective control of simulation runs by a new evaluation algorithm for correlated random sequences", in New Cost-Effective Systems, Networks and Services, ITC12, pp. 12561264.

[ 46 ] 1940. Shohat J. "Laguerre polynomials and the Laplace transform", Duke Math. J. 6:615626.

[ 47 ] 1976. Sidi A. "Best rational function approximation to Laplace transform inversion using a window function", J. Comput. Appl. Math. 2(3):187194.

[ 48 ] 1970. Silverberg M. "Improving the efficiency of Laplace transform inversion for network analysis", Electron Lett. 6:105-106.

[ 49 ] 1966. Spinelli R.A. "Numerical inversion of a Laplace transform", SIAM J. Numer.Anal. 3(4):636649.

[ 50 ] 1991. Steidl G. and M. Tasche. "A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms", Math. Comput., 56(193):281296.

[ 51 ] 1992. Strain J. "A fast Laplace transform based on Laguerre functions", Math. Comput., 58(197):275283.

[ 52 ] 1987. Van Iseghem J. "Laplace transform inversion and Padé-type approximants", North-Holland Applied Numerical Mathematics 3:529538.

[ 53 ] 1974. Veillon F. "Algorithm 486 [D5] : Numerical inversion of Laplace transform", Comm. ACM 17(10):587-589.

[ 54 ] 1955. Weiss G. "On the expansion of a function in terms of Laguerre polynomials", IRE Trans. Circuit Theory, CT2(Mars):104105.

[ 55 ] 1929. Widder D.V. : "A generalisation of Dirichlet's series and of Laplace's integral by means of a Stieljes integral", Trans. Amer. Math. Soc. 31(oct.):694743.

[ 56 ] 1931. Widder D.V. : "Necessary and sufficient conditions for the representation of a function by a Laplace integral", Trans. Amer. Math. Soc. 33(oct.):851892.

[ 57 ] 1934. Widder D.V. : "The inversion of the Laplace integral and the related moment problem", Trans. Amer. Math. Soc. 36(jan.):107186.

[ 58 ] 1954. Winkler S. "The approximation problem of network synthesis", IRE Trans. Circuit Theory, CT1(Sept.):520.

[ 59 ] 1969. Zakian V. "Numerical inversion of Laplace transform", Electron. Lett. 5(6):120-121.

[ 60 ] 1970. Zakian V. "Optimisation of numerical inversion of Laplace transform", Electron. Lett. 6(21):677-679.

[ 61 ] 1971. Zakian V. and Gannon D. R. "Leastsquares optimisation of numerical inversion of Laplace transform", Electron. Lett. 7(3):70-71.

3. Books

[ 62 ] 1966. Bellman R., R.E. Kalaba, and J.A. Lockett. "Numerical inversion of the Laplace transform : applications to biology, economics, engineering, and physics", American Elsevier, New York.

[ 63 ] 1980. Brezinski C. "Padé-type approximations and general orthogonal polynomials", Birkhäuser, Basel.

[ 64 ] 1941. Churchil R. V. "Fourier series", McGraw-Hill, New. York.

[ 65 ] 1943. Doetsch G. "Laplace transformation", Dover.

[ 66 ] 1971. Doetsch G. "Guide to the applications of the Laplace and Z-transforms," Van Nostrand Reinhold, London.

[ 67 ] 1964. Gelfand I.M. and Shilov G. E. "Generalized functions," Academic Press, New York.

[ 68 ] 1973. Graves-Morris P. R. (Ed.) "Padé approximants and their applications", Academic Press, London. En particulier : Longman I.M. : "Use of Padé table for approximate Laplace transform inversion", pp. 131-133.

[ 69 ] 1947. Guillemin E.A. "The mathematics of circuit analysis", John Willey & Son, New- York

[ 70 ] 1956. Lanczos C. "Applied analysis," Prentice-Hall, Englewood Cliffs NJ.

[ 71 ] 1957. Lanczos C. "Applied analysis," Pitman, London.

[ 72 ] 1972. Lavrentiev M. and Chabat B. "Méthodes de la théorie des fonctions d'une variable complexe", Mir, Moscou 728 p.

[ 73 ] 1954. Magnus W. and F. Oberhettinger "Formulas and theorems for the functions of mathematical physic. Chelsea, New York.

[ 74 ] ****. Murray, "Transformation de Laplace", Spiegel

[ 75 ] 1974. Sneddon I.N. "Use of integral transforms", McGraw-Hill, New York.

[ 76 ] 1959. Szego G. "Orthogonal polynomials", Am. Math. Soc., New York.

[ 77 ] 1956. Walsh J.L., "Interpolation and approximation by rational functions in the complex domain", Am. Math. Soc., Providence RI.

[ 78 ] 1946. Widder D.V. "The Laplace transform", Princeton University Press.

4. Others

[ 79 ] 1983. Brochet P. "Contribution à l'inversion numérique de la transformation de Laplace", thèse 3ème Cycle, Université de Lille.

[ 80 ] 1982. Van Iseghem J. "Application des approximants de type Padé", thèse 3ème cycle, Université de Lille I.

[ 81 ] 1988. Cheng, A.H-D., and E. Detournay. "A direct boundary element method for plane strain poroelasticity". Int. J. Num. Anal. Meth. Geomech. 12:551-572.

[ 82 ] 1989. Cheng, A.H-D., and K. Ou. "An efficient Laplace transform solution for multiaquifer systems". Water Resour. Res. 25:742-748.

[ 83 ] 1993. Cheng, A.H-D., and O.K. Niorohunfola. "Multilayered leaky aquifer systems: I. Pumping well solution". Water Resour. Res. 29 :2787-2800.

[ 84 ] 1970. Chiu R.F., C.F. Chen and C.J. Huang. "A new method for the inverse Laplace transformation via the FFT (fast Fourier transform)", 22th Southwestern IEEE Conf. Record, Dallas, Texas, 201203.

[ 85 ] 1967. Cooley J.W., P.A.W. Lewis and P.D. Welch. "Application of the FFT (fast Fourier transform) to computation of Fourier integrals, Fourier series and convolution integrals", IEEE Trans. AE-15 (1967), 79-85.

[ 86 ] 1964. Cost T. L. "Approximate Laplace transform inversions in viscoelastic stress analysis", AIAA J. 2:2157-2166.

[ 87 ] 1988. Detournay, E. and A.H-D. Cheng. "Porroelastic response of a borehole in a non-hydrostatic stress field", Int. J. Rock , Mech. Min. Sci. Geomech. Abstr. 25:171-l82.

[ 88 ] 1943. Erdèly A. Philos. Mag. 34:533-537.

[ 89 ] 1988. Garbow B.S., Giunta G., Lyness J. N. and Murli A. "Algorithm 662. A software package for the inversion of the Laplace transform, Weeks' method", ACM Trans. Math. Soft. 14:171-176. (no. 2, Jun. 1988).

[ 90 ] 1966. Gentleman W.M. and G. Sande. "FFT (fast Fourier transforms) for fun and profit", Proc. AFIPS 1966 Fall Joint Comput. Confer., Vol. 29, pp. 563-578.

[ 91 ] 1990. Harrison. J. "", Applied Probab. 27(1):7487.

[ 92 ] 1991. Hwang. "", Comput and Math with applic 1991 1:1324.

[ 93 ] 1833. Murphy R. "", Camb. Phil. Trans. 4:353.

[ 94 ] 1982. Narayanan G.V., and D.E. Beskos. "Numerical operational methods for the time-dependent linear problems". Int. J. Numer. Meth. Engng. 18:1829-1854.

[ 95 ] 1935. Picone M. "", Rend. Lincei, 21(6):306.

[ 96 ] 1969. Piessens R. "", Nordisk Tidskr. Informalionsbehandling 9:351-361.

[ 97 ] 1971. Piessens R. and M. Branders "", Proc, IEE 118:1517-1522.

[ 98 ] 1972. Piessens R. "", J. Inst. Math. Appl. 10:185-192.

[ 99 ] 1970. Rizzo F. J. and Shippy D. J. "", AIAA J. 8:2004-2009.

[ 100 ] 1958. Salzer H.E. "Tables for the numerical calculation of inverse Laplace transforms", J. Math. and Phys. 37:89-109.

[ 101 ] 1961. Salzer H.E. "Additional formulas and tables for orthogonal polynomials originating from inversion integral", J. Math. and Phys. 40:7286.

[ 102 ] 1962. Schapery R.A. "", Proc. 4th U.S. Nat. Congr. Appl. Mech., ASME 2:1075-1085.

[ 103 ] 1961. Shirtliffe C.J. and Stephenson D. G. "A Computer Oriented Adaptation Of Salzer's Method For Inverting Laplace Transforms", J. Math. and Phys. 40:135-141.

[ 104 ] 1972. Simon R.M., M.T. Stroot and G.H. Weiss. "Numerical Inversion of Laplace Transforms with Application to Percentage Labeled Mitoses Experiments", Computers and Biomed. Res. 5:596607.

[ 105 ] 1975. Singhal V. and Vlach J. "", J. Franklin Inst. 299:109-126.

[ 106 ] 1951. Ter Haar D. "", J. Polymer Sci. 6:247.

[ 107 ] 1935. Tricomi F. "", R. C. Accad. Nat. dei Lincei 21:232-239 et 420

[ 108 ] 19xx. xxx