Periodic and reverse periodic continued fractions.
نویسندگان
چکیده
منابع مشابه
Periodic Continued Fractions And
We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
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We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form φ(λ) = [b0; b1, b2, . . . , bN ]α = b0 + λ− α1 b1 + λ−α2 b2+ . . .bN−1+ λ−αN bN+ λ−α1 b1+ λ−α2 b2+ . . . , for some fixed sequence αi. We show that this problem has a natural answer given...
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We construct all families of quartic polynomials over Qwhose square root has a periodic continued fraction expansion, and detail those expansions. In particular we prove that, contrary to expectation, the cases of period length nine and eleven do not occur. We conclude by providing a list of examples of pseudo-elliptic integrals involving square roots of polynomials of degree four. The primary ...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1960
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998338