logarithmic residue
1Logarithmic derivative — In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where f ′ is the derivative of f. When f is a function f(x) of a real variable x, and takes real, strictly… …
2Logarithmic form — Any formula written in terms of logarithms may be said to be in logarithmic form.Logarithmic differential formsIn contexts including complex manifolds and algebraic geometry, a logarithmic differential form is a 1 form that, locally at least, can …
3Argument principle — In complex analysis, the Argument principle (or Cauchy s argument principle) states that if f ( z ) is a meromorphic function inside and on some closed contour C , with f having no zeros or poles on C , then the following formula holds: oint {C}… …
4Renato Caccioppoli — (pronounced|katˈtʃɔpːoli) (20 January, 1904 – 8 May, 1959) was a noted Italian mathematician.BiographyBorn in Naples, Italy, he was the son of Giuseppe Caccioppoli (1852 1947), a noted Neapolitan surgeon, and his second wife Sofia Bakunin (1870… …
5Prime number theorem — PNT redirects here. For other uses, see PNT (disambiguation). In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are… …
6Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… …
7Polylogarithm — Not to be confused with polylogarithmic. In mathematics, the polylogarithm (also known as Jonquière s function) is a special function Lis(z) that is defined by the infinite sum, or power series: It is in general not an elementary function, unlike …
8List of complex analysis topics — Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied …
9Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …
10Differential of the first kind — In mathematics, differential of the first kind is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic geometry), for everywhere regular differential 1… …
