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The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form ...

The term "indeterminate" is sometimes used as a synonym for unknown or variable (Becker and Weispfenning 1993, p. 188). A mathematical expression can also be said to be ...

A sequence is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, a sequence S_n converges to the limit S lim_(n->infty)S_n=S if, ...

Delta_hf(x)=(f(x+h)-f(x))/h=(Deltaf)/h. It gives the slope of the secant line passing through f(x) and f(x+h). In the limit h->0, the difference quotient becomes the partial ...

Let a sequence {a_i}_(i=1)^infty be strictly increasing and composed of nonnegative integers. Call A(x) the number of terms not exceeding x. Then the density is given by ...

The integral transform (Kf)(x)=Gamma(p)int_0^infty(x+t)^(-p)f(t)dt. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...