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A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

The sign of a real number, also called sgn or signum, is -1 for a negative number (i.e., one with a minus sign "-"), 0 for the number zero, or +1 for a positive number (i.e., ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

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 ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

Pairs of partitions for a single number whose Ferrers diagrams transform into each other when reflected about the line y=-x, with the coordinates of the upper left dot taken ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...