Search Results for "Beta Function"

de Rham's function is the function defined by the functional equations phi_alpha(1/2x) = alphaphi_alpha(x) (1) phi_alpha(1/2(x+1)) = alpha+(1-alpha)phi_alpha(x) (2) (Trott ...

The generalized hypergeometric function F(x)=_pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;x] satisfies the equation where theta=x(partial/partialx) is the ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

The Weierstrass zeta function zeta(z;g_2,g_3) is the quasiperiodic function defined by (dzeta(z;g_2,g_3))/(dz)=-P(z;g_2,g_3), (1) where P(z;g_2,g_3) is the Weierstrass ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

rho_n(nu,x)=((1+nu-n)_n)/(sqrt(n!x^n))_1F_1(-n;1+nu-n;x), where (a)_n is a Pochhammer symbol and _1F_1(a;b;z) is a confluent hypergeometric function of the first kind.