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Symbolic expression of the quotient of a continued fraction

asked 2021-08-23 11:56:20 +0100

oldani gravatar image


Is it possible to get the symbolic expression of the numerator and denominator $p_n(a_0,...,a_n$ and $q_n(a_0,...,a_n)$ of the partial quotients of a continued fraction?

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answered 2021-08-23 21:43:18 +0100

Max Alekseyev gravatar image

updated 2021-08-23 21:59:13 +0100

Such expressions are given by continuants - namely, $p_n(a_0,\dots,a_n)= K_{n+1}(a_0,\dots,a_n)$ and $q_n(a_0,\dots,a_n)= K_n(a_1,\dots,a_n)$ . Sage provides function continuantfor computing them - see

Here is an example for $n=5$:

R.<a> = InfinitePolynomialRing(QQ)
print('p=', continuant( [a[i] for i in (0..5)]) )
print('q=', continuant( [a[i] for i in (1..5)]) )
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Asked: 2021-08-23 11:56:20 +0100

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Last updated: Aug 23 '21