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On the expected length of an orderly path

Author

Listed:
  • Martin Wiegand

    (University College London)

  • Saralees Nadarajah

    (Howard University
    University of Manchester)

Abstract

Lutz et al. (Ann Oper Res 289:463–472, 2020) derived an integral expression for the expected length of an orderly path. We show here that the integral expression can be reduced to a closed form expression in terms of the Gauss hypergeometric function, a generalised hypergeometric function and the Appell hypergeometric function of the first kind. We check the correctness of the closed form expression numerically as well as provide a Mathematica code. Finally, we show that the closed form expression is more efficient than known integral expressions.

Suggested Citation

  • Martin Wiegand & Saralees Nadarajah, 2024. "On the expected length of an orderly path," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 963-971, June.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:2:d:10.1007_s12597-023-00709-1
    DOI: 10.1007/s12597-023-00709-1
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    References listed on IDEAS

    as
    1. Trevor S. Hale & Faizul Huq & Heather Lutz & Carles Moslares, 2015. "On the expected distance of a random walk," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 241-250.
    2. Heather S. Lutz & Trevor S. Hale & Faizul Huq, 2020. "Technical note: the expected length of an orderly path," Annals of Operations Research, Springer, vol. 289(2), pages 463-472, June.
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    1. Heather S. Lutz & Trevor S. Hale & Faizul Huq, 2020. "Technical note: the expected length of an orderly path," Annals of Operations Research, Springer, vol. 289(2), pages 463-472, June.

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