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The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

I((chi_s^2)/(sqrt(2(k-1))),(k-3)/2)=(Gamma(1/2chi_s^2,(k-1)/2))/(Gamma((k-1)/2)), where Gamma(x) is the gamma function.

If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

The l^infty-polynomial norm defined for a polynomial P=a_kx^k+...+a_1x+a_0 by ||P||_infty=max_(k)|a_k|. Note that some authors (especially in the area of Diophantine ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

A probabilistic experiment is an occurrence such as the tossing of a coin, rolling of a die, etc. in which the complexity of the underlying system leads to an outcome that ...

A precise sequence of instructions designed to accomplish a given task. The implementation of an algorithm on a computer using a programming language is an example of a ...

A statistical test making use of the statistical ranks of data points. Examples include the Kolmogorov-Smirnov test and Wilcoxon signed rank test.

The kernel of a ring homomorphism f:R-->S is the set of all elements of R which are mapped to zero. It is the kernel of f as a homomorphism of additive groups. It is an ideal ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...