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A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

A handlebody of type (n,k) is an n-dimensional manifold that is attained from the standard n-disk by attaching only k-D handles.

Various handshaking problems are in circulation, the most common one being the following. In a room of n people, how many different handshakes are possible? The answer is (n; ...

The contour C_epsilon illustrated above.

There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) ...

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 ...

H_n^((2))(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 the second kind. Hankel functions of the second kind ...

A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

The Hankel transform (of order zero) is an integral transform equivalent to a two-dimensional Fourier transform with a radially symmetric integral kernel and also called the ...

J_m(x)=(x^m)/(2^(m-1)sqrt(pi)Gamma(m+1/2))int_0^1cos(xt)(1-t^2)^(m-1/2)dt, where J_m(x) is a Bessel function of the first kind and Gamma(z) is the gamma function. Hankel's ...