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A point p on a regular surface M in R^3 is said to be hyperbolic if the Gaussian curvature K(p)<0 or equivalently, the principal curvatures kappa_1 and kappa_2, have opposite ...

A catastrophe which can occur for three control factors and two behavior axes. The hyperbolic umbilic is the universal unfolding of the function germ f(x,y)=x^3+y^3. The ...

The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...

Given a hypergeometric series sum_(k)c_k, c_k is called a hypergeometric term (Koepf 1998, p. 12).

The operator I^~ which takes a real number to the same real number I^~r=r.

The identric mean is defined by I(a,b)=1/e((b^b)/(a^a))^(1/(b-a)) for a>0, b>0, and a!=b. The identric mean has been investigated intensively and many remarkable inequalities ...

The term "ill-defined" is also used informally to mean ambiguous.

A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed.

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that ...

The axis in the complex plane corresponding to zero real part, R[z]=0.