A Continued Fraction
![\begin{displaymath}
\sigma=a_0+{\strut\displaystyle b_1\over{\strut\displaystyle...
...\strut\displaystyle b_3\over\strut\displaystyle a_3+\ldots}}}}
\end{displaymath}](s1_1148.gif) |
(1) |
in which the
s are all unity, leaving a continued fraction of the form
![\begin{displaymath}
\sigma = a_0+{1\over{\strut\displaystyle a_1+{\strut\display...
...{\strut\displaystyle 1\over\strut\displaystyle a_3+\ldots}}}}.
\end{displaymath}](s1_1150.gif) |
(2) |
A simple continued fraction can be written in a compact abbreviated Notation as
![\begin{displaymath}
\sigma=[a_0, a_1, a_2, a_3, \ldots].
\end{displaymath}](s1_1151.gif) |
(3) |
Bach and Shallit (1996) show how to compute the Jacobi Symbol in terms of the simple continued fraction of a
Rational Number
.
See also Continued Fraction
References
Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA:
MIT Press, pp. 343-344, 1996.
© 1996-9 Eric W. Weisstein
1999-05-26