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Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

A commutative diagram is a collection of maps A_i-->^(phi_i)B_i in which all map compositions starting from the same set A and ending with the same set B give the same ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...