Porter's Constant

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

The constant appearing in Formulas for the efficiency of the Euclidean Algorithm,

$$C = {6\ln 2\over\pi^2}\left[{3\ln 2+4\gamma-{24\over\pi^2}\zeta'(2)-2}\right]-{1\over 2}$$

$$= 1.4670780794\ldots,$$

where $\gamma$ is the Euler-Mascheroni Constant and $\zeta(z)$ is the Riemann Zeta Function.

See also Euclidean Algorithm

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/porter/porter.html

Porter, J. W. ``On a Theorem of Heilbronn.'' Mathematika 22, 20-28, 1975.