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The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

The doublestruck capital letter Z, Z, denotes the ring of integers ..., -2, -1, 0, 1, 2, .... The symbol derives from the German word Zahl, meaning "number" (Dummit and Foote ...

Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

A sequence whose terms are integers. The most complete printed references for such sequences are Sloane (1973) and its update, Sloane and Plouffe (1995). Neil Sloane ...

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

The cotangent function cotz is the function defined by cotz = 1/(tanz) (1) = (i(e^(iz)+e^(-iz)))/(e^(iz)-e^(-iz)) (2) = (i(e^(2iz)+1))/(e^(2iz)-1), (3) where tanz is the ...