 About 13,400 results  books.google.com Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today. 

 books.google.com 10.8 Euler's constant, symbol γ Euler's constant was first introduced by Euler in
1734 as the limit [Eul48] γ := lim n→∞ ( n∑k=1 1 k − ln(n) ) = 0.57721566490153
.... (10.8.1) It is also known as the EulerMascheroni constant. It is closely related
... 

 books.google.com fractions. For example, with a0 = 0, a1 = z, a2 = −z2/3, a3 = −3z2/5, ... , we find
that arctanz = z − z3 3 + z5 5 − z7 7 + z9 9 −··· (9.7) with z ≤ 1, can be
expressed as an irregular continued fraction due to Euler: arctanz =z1+ z2 3−z2 +
9z2 5−3z2 ... 

 books.google.com We usually see continued fractions in which all the numerators are 1. As Euler
will note soon, for such continued fractions, the rule is a good deal simpler. Euler
does a few explicit calculations to find the difference between consecutive terms,
... 

 books.google.com Lorentzen [16] has an alternative approach to Ramanujan's continued fractions.
Ramanujan was a master of manipulatorics in the class of Euler himself. Thus it is
appropriate that the continued fraction formulas of Ramanujan here are all ... 

 books.google.com Our purpose in this month's column is to look at what Euler did, and to see just
how rigorous Euler' s results were. Euler and Lambert both used the tools of
continued fractions to produce their results. Euler's 1737 article that MacTutor
mentions ... 

 books.google.com [Khru06a] S. Khrushchev, A recovery of Brouncker's proof of the quadrature
continued fraction, Publications Mathematiques 50(1) (2006), 3–42. [Khru06b] S.
Khrushchev, On Euler's differential methods for continued fractions, Electr. Trans. 

 books.google.com Based on earlier work of his predecessors, Euler began his research on
continued fractions and published many new ideas and results in his first paper
entitled, “De Fractionibus Continuis” in 1737. He also proved that any rational
number can ... 

 books.google.com we have U0 + Ul + ' ' ' + un = ^ (1.50) 1 unu 0"2 u + u  "n2"n This is Euler's
famous transformation of a series into a continued fraction which we shall use to
derive a most convenient algorithm for the efficient evaluation of a continued
fraction. 

 books.google.com Continued fractions are part of the "lost mathematics," the mathematics now
considered too advanced for high school and too elementary for college. (Petr
Beckman)1 ... epitomized by Euler's continued fractions for e. Whorled figures are
the ... 

 