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The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

The n-pan graph is the graph obtained by joining a cycle graph C_n to a singleton graph K_1 with a bridge. The n-pan graph is therefore isomorphic with the (n,1)-tadpole ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

Q(n), also denoted q(n) (Abramowitz and Stegun 1972, p. 825), gives the number of ways of writing the integer n as a sum of positive integers without regard to order with the ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...