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A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The plots above show the values of the function obtained by taking the natural logarithm of the gamma function, lnGamma(z). Note that this introduces complicated branch cut ...

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...