Search Results for ""

Let gamma be a path in C, w=f(z), and theta and phi be the tangents to the curves gamma and f(gamma) at z_0 and w_0. If there is an N such that f^((N))(z_0) != 0 (1) ...

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

The Pauli matrices, also called the Pauli spin matrices, are complex matrices that arise in Pauli's treatment of spin in quantum mechanics. They are defined by sigma_1 = ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...

A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The ...

A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type {mu} and forms from them ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...