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The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

The portion of the complex plane z=x+iy with real part R[z]>0.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

The symbol used by engineers and some physicists to denote i, the imaginary number sqrt(-1). j is probably preferred over i because the symbol i (or I) is commonly used to ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

U_n(f)=int_a^bf(x)K_n(x)dx, where {K_n(x)} is a sequence of continuous functions.

A function f which may (but does not necessarily) associate a given member of the range of f with more than one member of the domain of f. For example, trigonometric ...