Search Results for ""

A special function psi_1(z) corresponding to a polygamma function psi_n(z) with n=1, given by psi_1(z)=(d^2)/(dz^2)lnGamma(z). (1) An alternative function ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

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

There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given ...

The Weierstrass substitution is the trigonometric substitution t=tan(theta/2) which transforms an integral of the form intf(costheta,sintheta)dtheta into one of the form ...

e^(i(ntheta))=(e^(itheta))^n. (1) From the Euler formula it follows that cos(ntheta)+isin(ntheta)=(costheta+isintheta)^n. (2) A similar identity holds for the hyperbolic ...