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    Eltayeb, Hassan and Mesloub, Said 2014. Exact Evaluation of Infinite Series Using Double Laplace Transform Technique. Abstract and Applied Analysis, Vol. 2014, p. 1.


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  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 41, Issue 4
  • April 2000, pp. 473-486

Summing series arising from integro-differential-difference equations

  • P. Cerone (a1) and A. Sofo (a1)
  • DOI: http://dx.doi.org/10.1017/S0334270000011772
  • Published online: 17 February 2009
Abstract

By applying Laplace transform theory to solve first-order homogeneous differential-difference equations it is conjectured that a resulting infinite sum of a series may be expressed in closed form. The technique used in obtaining a series in closed form is then applied to other examples in teletraffic theory and renewal processes.

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[1]R. Bellman and K. L. Cooke , Differential-Difference Equations (Academic Press, New York, 1963).

[2]D. M. Bloom , “Advanced problem 6652”, American Mathematical Monthly 98 (1991) 272273.

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[4]B. Braden , “Calculating sums of infinite series”, American Mathematical Monthly 99 (1992) 649655.

[5]F. Brauer , “Absolute stability in delay equations”, J. Diff. Eq. 69 (1987) 185191.

[6]F. Brauer and M. Zhien , “Stability of stage-structured population models”, J. Math. Anal. Appl. 126 (1987) 301315.

[9]K. L. Cooke and Z. Grossman , “Discrete delay, distributed delay and stability switches”, J. Math. Anal. Appl. 86 (1982) 592627.

[11]R. D. Driver , D. W. Sasser and M. L. Slater , “The equation with “small” delay”, American Mathematical Society 80 (1973) 990995.

[15]J. K. Hale and S. M. Yerduyn Lunel , Introduction to Functional Differential Equations (Springer, New York, 1993).

[16]D. Y. Hao and F. Brauer , “Analysis of a characteristic equation”, J. Integral Eq. Appl. 3 (1991) 239253.

[25]F. S. Wheeler , “Two differential-difference equations arising in number theory”, Trans. American Math. Soc. 318 (1990) 491523.

[28]E. M. Wright , “Stability criteria and the real roots of a transcendental equation”, J. Soc. Indust. Appl. Math. 9 (1961) 136148.

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