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Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

Hadjicostas's formula is a generalization of the unit square double integral gamma=int_0^1int_0^1(x-1)/((1-xy)ln(xy))dxdy (1) (Sondow 2003, 2005; Borwein et al. 2004, p. 49), ...

Porter's constant is the constant appearing in formulas for the efficiency of the Euclidean algorithm, C = (6ln2)/(pi^2)[3ln2+4gamma-(24)/(pi^2)zeta^'(2)-2]-1/2 (1) = ...

The Lagrange interpolating polynomial is the polynomial P(x) of degree <=(n-1) that passes through the n points (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n)), and ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

The secant numbers S_k, also called the zig numbers or the Euler numbers E_n^*=|E_(2n)| numbers than can be defined either in terms of a generating function given as the ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...