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Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...

Linear Algebra

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over GF(2) ("of order two"), illustrated above. It is a block design with nu=7, ...

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that ...

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

If a function f has a pole at z_0, then the negative power part sum_(j=-k)^(-1)a_j(z-z_0)^j (1) of the Laurent series of f about z_0 sum_(j=-k)^inftya_j(z-z_0)^j (2) is ...