“Porter's constant”的意思、由来-开放百科全书

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Porter's constant

释义

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In mathematics, Porter's constant C arises in the study of the efficiency of the Euclidean algorithm.^[1]^[2] It is named after J. W. Porter of University College, Cardiff.

Euclid's algorithm finds the greatest common divisor of two positive integers {{mvar|m}} and {{mvar|n}}. Hans Heilbronn proved that the average number of iterations of Euclid's algorithm, for fixed {{mvar|m}} and averaged over all choices of relatively prime integers {{mvar|n}},

Porter showed that the error term in this estimate is a constant, plus a polynomially-small correction, and Donald Knuth evaluated this constant to high accuracy. It is:

where

is the Euler–Mascheroni constant

is the Riemann zeta function

is the Glaisher–Kinkelin constant

References

1. ^{{citation | last = Knuth | first = Donald E. | authorlink = Donald E. Knuth | doi = 10.1016/0898-1221(76)90025-0 | issue = 2 | journal = Computers & Mathematics with Applications | pages = 137–139 | title = Evaluation of Porter's constant | volume = 2 | year = 1976}}
2. ^{{citation | last = Porter | first = J. W. | doi = 10.1112/S0025579300004459 | issue = 1 | journal = Mathematika | mr = 0498452 | pages = 20–28 | title = On a theorem of Heilbronn | volume = 22 | year = 1975}}.

2 : Mathematical constants|Analytic number theory

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