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The extension ring obtained from a commutative unit ring (other than the trivial ring) when allowing division by all non-zero divisors. The ring of fractions of an integral ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called hyperbolic if the matrix Z=[A B; B C] (2) ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

A ring of fractions that coincides with the localization with respect to the set of all non-zero divisors.

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

A number of closed-form constants can be obtained for generalized continued fractions having particularly simple partial numerators and denominators. The Ramanujan continued ...