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int_0^z(t^mu)/(1+t)dt=z/(mu+1+((mu+1)^2z)/((mu+2)-(mu+1)z+((mu+2)^2z)/((mu+3)-(mu+2)z+...))) for mu>-1 and -1<z<=1 (Perron 1954-1957, p. 18; Borwein et al. 2004, p. 35).

f(x)=1/x-|_1/x_| for x in [0,1], where |_x_| is the floor function. The natural invariant of the map is rho(y)=1/((1+y)ln2).

An algorithm for computing an Egyptian fraction.

A proper fraction is a fraction p/q with p,q>0 such that p/q<1. A fraction p/q>1 is called an improper fraction.

The continued fraction ((x+1)^n-(x-1)^n)/((x+1)^n+(x-1)^n)=n/(x+)(n^2-1)/(3x+)(n^2-2^2)/(5x+...).

A complex fraction is a fraction in which numerator, denominator, or both are themselves fractions, for example (2/3)/(4/5).

A fraction p/q>=1. A fraction with p/q<1 is called a proper fraction. Therefore, the special cases 1/1, 2/2, 3/3, etc. are generally considered to be improper.

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

A fraction a/b written in lowest terms, i.e., by dividing numerator and denominator through by their greatest common divisor (a,b). For example, 2/3 is the reduced fraction ...

A common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions. For example, 2/5 is a common fraction, while (1/3)/(2/5) is ...