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The Fox H-function is a very general function defined by where 0<=m<=q, 0<=n<=p, alpha_j,beta_j>0, and a_j,b_j are complex numbers such that no pole of Gamma(b_j-beta_js) for ...

The so-called generalized Fourier integral is a pair of integrals--a "lower Fourier integral" and an "upper Fourier integral"--which allow certain complex-valued functions f ...

A square matrix is called Hermitian if it is self-adjoint. Therefore, a Hermitian matrix A=(a_(ij)) is defined as one for which A=A^(H), (1) where A^(H) denotes the conjugate ...

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the ...

Although Descartes originally used the term "imaginary number" to refer to what is today known as a complex number, in standard usage today, "imaginary number" means a ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A polar representation of a complex measure mu is analogous to the polar representation of a complex number as z=re^(itheta), where r=|z|, dmu=e^(itheta)d|mu|. (1) The analog ...