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Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

A function that joins univariate distribution functions to form multivariate distribution functions. A two-dimensional copula is a function C:I^2->I such that C(0,t)=C(t,0)=0 ...

A root-finding algorithm used in LU decomposition. It solves the N^2 equations i<j l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ii)u_(ij)=a_(ij)i=j ...

The evolute of a deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid evolute for n=3 x_e = 2cost-cos(2t) (3) y_e = 2sint+sin(2t), (4) which is ...

The involute of the deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid involute for n=3 x_i = 1/9[2cost-cos(2t)] (3) y_i = 1/9[2sint+sin(2t)], (4) ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

A method which can be used to solve any quadratic congruence equation. This technique relies on the fact that solving x^2=b (mod p) is equivalent to finding a value y such ...

A knot or link L^n in S^(n+2) is said to be fibered if there exists a fibration f:S^(n+2)-L->S^1 and if the fibration is well-behaved near L (Rolfsen 1976, p. 323). Examples ...

The flattening of a spheroid (also called oblateness) is denoted epsilon or f (Snyder 1987, p. 13). It is defined as epsilon={(a-c)/a=1-c/a oblate; (c-a)/a=c/a-1 prolate, (1) ...

F_x[cos(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)+e^(-2piik_0x))/2)dx (1) = 1/2int_(-infty)^infty[e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...