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A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

To enumerate a set of objects satisfying some set of properties means to explicitly produce a listing of all such objects. The problem of determining or counting all such ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

The gamma product (e.g., Prudnikov et al. 1986, pp. 22 and 792), is defined by Gamma[a_1,...,a_m; b_1,...,b_n]=(Gamma(a_1)...Gamma(a_m))/(Gamma(b_1)...Gamma(b_n)), where ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) ...

A rational polynomial is a polynomial having rational coefficients. While the term "rational polynomial" is sometimes used as a synonym for rational function, this usage is ...

The solution u(x,y)=int_0^xdxiint_1^yR(xi,eta;x,y)f(xi,eta)deta, where R(x,y;xieta) is the Riemann function of the linear Goursat problem with characteristics phi=psi=0 ...

A generalization of the Bessel differential equation for functions of order 0, given by zy^('')+y^'+(z+A)y=0. Solutions are y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz), where ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...