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Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation t^3+2t^2-t-1=0, (1) then the Rogers L-function satisfies L(alpha)-L(alpha^2) = 1/7 (2) ...

_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)] ...

The Rogers-Ramanujan continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894, Ramanujan 1957, ...

Given a Taylor series f(z)=sum_(n=0)^inftyC_nz^n=sum_(n=0)^inftyC_nr^ne^(intheta), (1) where the complex number z has been written in the polar form z=re^(itheta), examine ...

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure theta = ...

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos(theta/2) and ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of 90 degrees, 180 degrees, and 270 ...