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Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

For a scalar function f over a surface parameterized by u and v, the surface integral is given by Phi = int_Sfda (1) = int_Sf(u,v)|T_uxT_v|dudv, (2) where T_u and T_v are ...

Plotting l_x from a life expectancy table on a logarithmic scale versus x gives a curve known as a survivorship curve. There are three general classes of survivorship curves, ...

If f:M->N, then the tangent map Tf associated to f is a vector bundle homeomorphism Tf:TM->TN (i.e., a map between the tangent bundles of M and N respectively). The tangent ...

A Thue equation is a Diophantine equation of the form A_nx^n+A_(n-1)x^(n-1)y+A_(n-2)x^(n-2)y^2+...+A_0y^n=M in terms of an irreducible polynomial of degree n>=3 having ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

The triangular grid graph T_n is the lattice graph obtained by interpreting the order-(n+1) triangular grid as a graph, with the intersection of grid lines being the vertices ...

An upper triangular matrix U is defined by U_(ij)={a_(ij) for i<=j; 0 for i>j. (1) Written explicitly, U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... ...