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J_n(x)=1/piint_0^picos(ntheta-xsintheta)dtheta, where J_n(x) is a Bessel function of the first kind.

If m is an integer, then for every residue class r (mod m), there are infinitely many nonnegative integers n for which P(n)=r (mod m), where P(n) is the partition function P.

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

A generalization of the hypergeometric function identity (1) to the generalized hypergeometric function _3F_2(a,b,c;d,e;x). Darling's products are (2) and (3) which reduce to ...

The Fourier transform of the constant function f(x)=1 is given by F_x[1](k) = int_(-infty)^inftye^(-2piikx)dx (1) = delta(k), (2) according to the definition of the delta ...

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

J_m(x)=(2x^(m-n))/(2^(m-n)Gamma(m-n))int_0^1J_n(xt)t^(n+1)(1-t^2)^(m-n-1)dt, where J_m(x) is a Bessel function of the first kind and Gamma(x) is the gamma function.

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...