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The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

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), ...

Integration by parts is a technique for performing indefinite integration intudv or definite integration int_a^budv by expanding the differential of a product of functions ...

N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals a_k=int_1^2((lnx)^k)/(x-1)dx. (1) They found the values for k=1 and 2. The general constants for k>3 ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...