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Calculus I

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

An entire function which is a generalization of the Bessel function of the first kind defined by J_nu(z)=1/piint_0^picos(nutheta-zsintheta)dtheta. Anger's original function ...

The integral int_0^1x^p(1-x)^qdx, called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.

The inverse erf function is the inverse function erfc^(-1)(z) of erfc(x) such that erfc(erfc^(-1)(x))=erfc^(-1)(erfc(x)), (1) with the first identity holding for 0<x<2 and ...