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Date: 30-5-2020
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Porter's constant is the constant appearing in formulas for the efficiency of the Euclidean algorithm,
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(OEIS A086237), where is the Euler-Mascheroni constant, is the Riemann zeta function, and is the Glaisher-Kinkelin constant (Knuth 1998, p. 357). The notation is generally used for this constant (Knuth 1998, p. 357, Finch 2003, pp. 156-157), though other authors use (Ustinov 2010) or (Dimitrov et al. 2000).
The related constant originally considered by Porter (1975) and Knuth (1976) was denoted and , respectively, and defined by
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Knuth (1976) suggested be called the Lochs-Porter constant due to the work of Lochs (1961).
REFERENCES:
Dimitrov, V. S.; Jullien, G. A.; and Miller, W. C. "Complexity and Fast Algorithms for Multiexponentiations." IEEE Trans. Comput. 49, 141-147, 2000.
Finch, S. R. "Porter-Hensley Constants." §2.18 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 156-160, 2003.
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 113, 2003.
Knuth, D. E. "Evaluation of Porter's Constant." Computers Math. Appl. 2, 137-139, 1976.
Knuth, D. E. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd ed. Reading, MA: Addison-Wesley, 1998.
Lochs, G. "Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmässigen Kettenbrüche." Monatsh. f. Math. 65, 27-52, 1961.
Porter, J. W. "On a Theorem of Heilbronn." Mathematika 22, 20-28, 1975.
Sloane, N. J. A. Sequence A086237 in "The On-Line Encyclopedia of Integer Sequences."
Ustinov, A. V. "The Mean Number of Steps in the Euclidean Algorithm with Odd Partial Quotients." Math. Notes 88, 574-584, 2010.
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