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A Bessel function Z_n(x) is a function defined by the recurrence relations Z_(n+1)+Z_(n-1)=(2n)/xZ_n (1) and Z_(n+1)-Z_(n-1)=-2(dZ_n)/(dx). (2) The Bessel functions are more ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

The confocal ellipsoidal coordinates, called simply "ellipsoidal coordinates" by Morse and Feshbach (1953) and "elliptic coordinates" by Hilbert and Cohn-Vossen (1999, p. ...

Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...

Approximants derived by expanding a function as a ratio of two power series and determining both the numerator and denominator coefficients. Padé approximations are usually ...

The concept of "random close packing" was shown by Torquato et al. (2000) to be mathematically ill-defined idea that is better replaced by the notion of "maximally random ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...