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The Hankel functions of the first kind are defined as H_n^((1))(z)=J_n(z)+iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

A parametric latitude which gives a sphere equal surface area relative to an ellipsoid. The authalic latitude is defined by beta=sin^(-1)(q/(q_p)), (1) where ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

A compact manifold is a manifold that is compact as a topological space. Examples are the circle (the only one-dimensional compact manifold) and the n-dimensional sphere and ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

A distribution which arises in the study of half-integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)+1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)+1) = ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...