Search Results for ""

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

The complete elliptic integral of the first kind K(k), illustrated above as a function of the elliptic modulus k, is defined by K(k) = F(1/2pi,k) (1) = ...

where R[mu+nu-lambda+1]>0, R[lambda]>-1, 0<a<b, J_nu(x) is a Bessel function of the first kind, Gamma(x) is the gamma function, and _2F_1(a,b;c;x) is a hypergeometric ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The logarithmic derivative of a function f is defined as the derivative of the logarithm of a function. For example, the digamma function is defined as the logarithmic ...

An analytic function approaches any given value arbitrarily closely in any epsilon-neighborhood of an essential singularity.

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

An even Walsh function with sequency k defined by Cal(n,k)=W(n,2k+1).

An odd Walsh function with sequency k defined by Sal(n,k)=W(n,2k).