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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 ...

Also called Radau quadrature (Chandrasekhar 1960). A Gaussian quadrature with weighting function W(x)=1 in which the endpoints of the interval [-1,1] are included in a total ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

The transformation S[{a_n}_(n=0)^N] of a sequence {a_n}_(n=0)^N into a sequence {b_n}_(n=0)^N by the formula b_n=sum_(k=0)^NS(n,k)a_k, (1) where S(n,k) is a Stirling number ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...