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The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the ...

Let M(h) be the moment-generating function, then the cumulant generating function is given by K(h) = lnM(h) (1) = kappa_1h+1/(2!)h^2kappa_2+1/(3!)h^3kappa_3+..., (2) where ...

The function f(x)=1-2|x|^(1/2) for x in [-1,1]. The natural invariant is rho(y)=1/2(1-y).

A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The term domain has (at least) three different meanings in mathematics. The term domain is most commonly used to describe the set of values D for which a function (map, ...

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

The exsecant is a little-used trigonometric function defined by excsc(x)=cscx-1, where cscx is the cosecant.

Any bivariate distribution function with marginal distribution functions F and G satisfies max{F(x)+G(y)-1,0}<=H(x,y)<=min{F(x),G(y)}.

A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ...