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A tensor-like object which reverses sign under inversion. Given a transformation matrix A, A_(ij)^'=det|A|a_(ik)a_(jl)A_(kl), where det is the determinant. A pseudotensor is ...

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

A complex number z is said to be purely imaginary if it has no real part, i.e., R[z]=0. The term is often used in preference to the simpler "imaginary" in situations where z ...

A generalized conformal mapping.

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.

Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

Every continuous linear functional U[f] for f in C[a,b] can be expressed as a Stieltjes integral U[f]=int_a^bf(x)dw(x), where w(x) is determined by U and is of bounded ...

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

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

A definition of a function using a contour integral. Schläfli integrals may be converted into Rodrigues representations.