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Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...

An equation or formula involving transcendental functions.

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

Involving two variables, as opposed to many (multivariate), or one (univariate).

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

A set of functions {f_1(n,x),f_2(n,x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., int_Rf_1(m,x)f_1(n,x)dx = ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...

The curve y=1-e^(ax), illustrated above.

Factor analysis allows the determination of common axes influencing sets of independent measured sets. It is "the granddaddy of multivariate techniques (Gould 1996, pp. ...