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A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite. Different fields of mathematics have different ...
The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the Rogers–Ramanujan identities. It can be evaluated explicitly for a broad class of values of its argument. Domain coloring representation of the convergent of the function , where is ...
Wikimedia Commons has media related to Continued fractions. In mathematics, regular continued fractions play an important role in representing real numbers, and have a rich general theory touching on a variety of topics in number theory. Moreover, generalized continued fractions have important and interesting applications in complex analysis .
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
Periodic continued fractions are in one-to-one correspondence with the real quadratic irrationals. The correspondence is explicitly provided by Minkowski's question-mark function. That article also reviews tools that make it easy to work with such continued fractions. Consider first the purely periodic part
Print/export Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. For the continued fraction expansion. of a number, see simple ...
List of representations of. e. The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
Simple continued fraction. A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated) continued fraction like. or an infinite continued fraction like.