Continued Fraction

A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction, which may itself be simple or itself a continued fraction. If the process of nesting fractions this way terminates in a simple fraction the result is called a finite continued fraction, and if it continues indefinitely the result is an infinite continued fraction; the special case in which every numerator equals one and every denominator is a positive integer is called a simple, or regular, continued fraction. Any positive rational number can be written as a finite simple continued fraction, and any positive irrational number can be written as an infinite simple continued fraction. Different fields of mathematics favor different terminology: in number theory the unqualified term continued fraction usually means a simple continued fraction, with the broader case called a generalized continued fraction, while in complex analysis and numerical analysis the unqualified term usually refers to the broader, general case.