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A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

The ordinary differential equation y=xf(y^')+g(y^'), where y^'=dy/dx and f and g are given functions. This equation is sometimes also known as Lagrange's equation (Zwillinger ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

q-calculus or quantum calculus is a methodology comparable to the usual study of calculus but which is centered on the idea of deriving q-analogous results without the use of ...

The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

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 ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...

There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...