 About 13,700 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] 1 n→∞ k ( n∑ k=1 γ:= lim −ln(n) ) =0.57721566490153..
.. (10.8.1) It is also known as the EulerMascheroni constant. It is closely related
to ... 

 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 −ˇˇˇ (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 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 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 ... 

 books.google.com Euler's general method in [68, p. 1 38] leads to general Tfraction [119, Eq. (A. 28)
, p. 390] expansions instead of regular Cfraction expansions. For additional
related information on Euler's work on continued fractions, see [31, pp. 97109], [
65 ... 

 books.google.com An infinite continued fraction [a0 ;a 1 ,a 2 ,ˇˇˇ ,a n ,ˇˇˇ] is said to be convergent if lim
= a (3.5.6) n→∞ p n qn exists and a is called the value of the infinite continued
fraction. It can be shown that every real number a can be represented uniquely
by ... 

 books.google.com ... Princeton, NJ 08544, United States. (2013 Jan 29) School of Mathematics,
Tehran: On a continued fraction ... This leads to a continued fraction (though not a
simple continued fraction) for Euler's constant. It seems to be the first nontrivial ... 

 books.google.com In the continuous case one has to find, for a function y.x/, x 2 aIb, a polynomial f
of a certain maximum degree, such that ... In this article, Euler had given, for
example, a continued fraction representing the integral R 1 0 dx 1Cx . Except for
the ... 

 