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The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, inversion, or more ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

Trigonometric functions of npi/7 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 7 is not a ...

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

The Whittaker functions arise as solutions to the Whittaker differential equation. The linearly independent solutions to this equation are M_(k,m)(z) = ...