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Christoffel symbols of the second kind are the second type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. ...

Let there be n>=2 integers 0<a_1<...<a_n with GCD(a_1,a_2,...,a_n)=1. The values a_i represent the denominations of n different coins, where these denominations have greatest ...

The Jacobi triple product is the beautiful identity product_(n=1)^infty(1-x^(2n))(1+x^(2n-1)z^2)(1+(x^(2n-1))/(z^2))=sum_(m=-infty)^inftyx^(m^2)z^(2m). (1) In terms of the ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

The Pochhammer symbol (x)_n = (Gamma(x+n))/(Gamma(x)) (1) = x(x+1)...(x+n-1) (2) (Abramowitz and Stegun 1972, p. 256; Spanier 1987; Koepf 1998, p. 5) for n>=0 is an ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...

The algebraics, sometimes denoted A (Derbyshire 2004, p. 173), are the set of algebraic numbers. The set of algebraic numbers is implemented in the Wolfram Language as ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...