Examples of using Continued fractions in English and their translations into Danish
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he vindicated Cataldi by attributing the invention of continued fractions to him.
other topics in algebra, continued fractions, geometry and number theory.
Padé's doctoral supervisor Hermite had used approximants and continued fractions in his work of 1873 on proving the transcendence of e.
orthogonal polynomials and continued fractions, differential equations
summation of series, continued fractions and elliptic functions.
led him to prove the existence of a transcendental number in 1844 when he constructed an infinite class of such numbers using continued fractions.
He suggested that the end of Theodorus 's proof somehow involved the continued fractions for 17 and 19, a conjecture which is very much in line with modern ideas about Greek mathematics.
In 1949 Straus collaborated with Richard Bellman publishing Continued fractions, algebraic functions
In this Cotes explained gave a method of finding rational approximations as convergents of continued fractions, and the author of suggests that this explains how he found the approximation 44/37to the fourth root of 2 which we mentioned above.
their influence extended to Perron work on continued fractions Die Lehre von den Kettenbrüchen which was published in 1913.
their influence extended to Perron work on continued fractions Die Lehre von den Kettenbrüchen which was published in 1913.
The convergents for the continued fraction of r all satisfy this.
Stieltjes studied the continued fraction.
In 1655 he gave a continued fraction expansion of 4/π.
It deals with the development into a continued fraction of the generating function of a sequence satisfying a difference equation.
He also found a continued fraction expansion for the integral,
However Rawlins believes that a continued fraction method was used to calculate the value 11/83 while Fowler proposes that the anthyphairesis(or Euclidean algorithm) method was used see also.
In 1733 de Lagny examined the continued fraction expansion of the quotient of two integers
In 1655 he gave a continued fraction expansion of 4/π This result,
in 1894 he published a memoir in which he generalised the continued fraction algorithm which Hermite had studied in 1863