«CONTINUED FRACTION»に関連する英語の本
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Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions.
Aleksandr I͡Akovlevich Khinchin, Herbert Eagle, 1997
2
Handbook of
Continued Fractions for Special Functions
This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!
3
Elementary Number Theory: Primes, Congruences, and Secrets: ...
Corollary 5.3.11 (Convergence of continued fraction). Let a0,a1 ,... define a
simple continued fraction, and let x = [a0 ,a 1 ,...] ∈ R be its value. Then for all m,
∣ ∣ ∣ ∣ x − pm q m ∣ ∣ ∣ ∣ < 1 q m · q m+1 . Proposition 5.3.12. If x is a
rational ...
4
Encyclopedic Dictionary of Mathematics
Continued Fractions An alternative representation of a rational number by a
simple continued fraction is given by replacing bm above by (bm— 1)+1/1.
Examples of infinite simple continued fractions are where p is a natural number (
J. H. ...
5
Ergodic Theory of Numbers
5.4 Other continued fractions 5.4.1 Introduction Apart from the regular continued
fractions (RCF) an — at first sight — bewildering variety of continued fraction
expansions exist. Here we mention the continued fraction to the nearer integer ...
Karma Dajani, Cor Kraaikamp, 2002
6
An Invitation to Modern Number Theory
Formally write down the procedure to find the continued fraction expansion of x G
R. Note: By introducing two operators I(x) = * and F(x) = [x], one can write the
procedure in a manner similar to Horner's algorithm (see §1.2.2 and §7.1).
Exercise ...
Steven J. Miller, Ramin Takloo-Bighash, 2006
A continued fraction is one in which the denominator has been modified by the
addition of a fraction whose denominator has, in turn, been modified, etc.
Example — 1 2+1 5+1 7+1 3+1 2+1 This is usually written, for compactness, ...
Eliot K. Buckingham, Earle Buckingham, Holbrook L. Horton, 1981
conjugates-of an algebraic number, 134 continuant, 6, 76 continued fraction
algorithm-Hurwitz, 71 continued fraction Cantor set, 36, 145, 161, 163 continued
fraction expansion, 225, 229-231 continued fraction expansion-tanh(z), 225 ...
chain sequence, 90 Chebyshev polynomials, 42 chordal diameter, 71 chordal
distance, 55 chordal metric, 55 classical approximant, 6 classical convergence,
60 conjugate transformation, 174 continued fraction, 3 continued fraction
expansion, ...
chain sequence, 90 Chebyshev polynomials, 42 chordal diameter, 71 chordal
distance, 55 chordal metric, 55 classical approximant, 6 classical convergence,
60 conjugate transformation, 174 continued fraction, 3 continued fraction
expansion, ...
Lisa Lorentzen, Haakon Waadeland, 2008
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EVERYDAY EQUATIONS
In 1929, AA Krishnaswamy Ayyangar showed that the Chakravala algorithm corresponds to a so-called semi-regular continued fraction ... «mydigitalfc.com, 5月 15»
What's so Great about Continued Fractions?
Every number, rational or irrational, can be written as a continued fraction. In order to get a systematic way to write them, for now we're going to ... «Scientific American, 3月 15»
Pi Day: 8 Things About Your Favorite Mathematical Constant
continued fraction pi It's not as bad as it looks, I promise. Photo by Evelyn Lamb. Yegads, I know. But we can break it down step by step, look at ... «Slate Magazine, 3月 15»
Don't Recite Digits to Celebrate Pi. Recite Its Continued Fraction …
A couple years ago, I blogged about continued fractions, the most romantic way to represent numbers. As I wrote then, a continued fraction is ... «Scientific American, 3月 15»
Alberta PCs courting Wildrose defectors to capitalize on rift between …
I think the continued fraction on the direction of our leadership — I was in line with that direction, and they were not — and that was becoming ... «National Post, 11月 14»
Experts crack Ramanujan's algebra riddle
That result came to be known as the Rogers-Ramanujan continued fraction. Ramanujan died in 1920 before he could explain how he conjured ... «Times of India, 4月 14»
Mathematicians trace source of Rogers-Ramanujan identities, find …
That result came to be known as the Rogers-Ramanujan continued fraction. Hardy was astonished when he saw the formulas. "I had never ... «Phys.Org, 4月 14»
Happy Lévy Day
Lévy's constant is of interest mainly to those interested in numbers; it helps to describe the behavior of the continued fraction expansion of most ... «IEEE Spectrum, 3月 14»
Srinivasa Ramanujan: Genius acknowledged
Said he: "Ramanujan's procedure for obtaining a continued fraction expansion is one of successive reduction used in the work of the 15th ... «India Today, 1月 14»
Fraction Twists Time & Falls in Love with "Dark Horse Presents"
"These eight pages are totally better than his astonishingly-good work on all of ['Infinite Vacation'], so buckle up," continued Fraction. "This guy's ... «Comic Book Resources, 6月 13»
