analytic function
61Hurwitz zeta function — In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. It is formally defined for complex arguments s with Re( s )>1 and q with Re( q )>0 by:zeta(s,q) = sum {n=0}^infty frac{1}{(q+n)^{sThis series …
62Harmonic function — In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U rarr; R (where U is an open subset of R n ) which satisfies Laplace s equation,… …
63Heaviside step function — The Heaviside step function, H , also called the unit step function, is a discontinuous function whose value is zero for negative argument and one for positive argument.It seldom matters what value is used for H (0), since H is mostly used as a… …
64Motivic L-function — In mathematics, motivic L functions are a generalization of Hasse–Weil L functions to general motives over global fields. The local L factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v… …
65Prime-counting function — In mathematics, the prime counting function is the function counting the number of prime numbers less than or equal to some real number x cite book |first=Eric |last=Bach |coauthors=Shallit, Jeffrey |year=1996 |title=Algorithmic Number Theory… …
66Proof that holomorphic functions are analytic — In complex analysis, a field of mathematics, a complex valued function f of a complex variable z *is holomorphic at a point a iff it is differentiable at every point within some open disk centered at a , and* is analytic at a if in some open disk …
67Artin L-function — In mathematics, an Artin L function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G . These functions were introduced in the 1923 by Emil Artin, in connection with his research into class field theory.… …
68Auxiliary function — In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions which appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value… …
69Zeta function regularization — In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to superficially divergent sums. The technique is now commonly applied to problems in physics, but… …
70Zonal spherical function — In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K invariant vector in an… …
