Recursive algorithm for the fast calculation of the limit of derivatives at points of indeterminateness

  • Authors:

  • Helmut Kempelmann

  • Affiliations:

  • Lehrstuhl für Allgemeine Elektrotechnik und Datenfernverarbeitung, RWTH Aachen, Federal Republic of Germany

  • Venue:
  • ACM SIGSAM Bulletin
  • Year:
  • 1981

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Abstract

It is a common method in probability and queueing theory to gain the n-th moment E[Xn] of a random variable X with density function fX(x) by the n-th derivative of the corresponding Laplace transform L(s) at the point s = 0[EQUATION]Quite often we encounter indetermined expressions of the form 0/0 which normally are treated by the rule of L'Hospital. This is a time and memory consuming task requiring greatest common divisor cancellations. This paper presents an algorithm that calculates only those derivatives of numerator and denominator which do not equal zero when taking the limit /1/. The algorithm has been implemented in REDUCE /2/. It is simpler and more efficient than that one proposed by /3/.