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Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

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 = ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

If a contour in the complex plane is curved such that it separates the increasing and decreasing sequences of poles, then ...

One of the symbols { and } used in many different contexts in mathematics. Braces are used 1. To denote grouping of mathematical terms, usually as the outermost delimiter in ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A (Courant and Hilbert 1989, p. 9), i.e., ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

In number theory (e.g., Ivić 2003), the symbol log_kx is commonly used to mean the nested logarithm (also called the repeated logarithm or iterated logarithm) ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...