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rho_(2s)(n)=(pi^s)/(Gamma(s))n^(s-1)sum_(p,q)((S_(p,q))/q)^(2s)e^(2nppii/q), where S_(p,q) is a Gaussian sum, and Gamma(s) is the gamma function.

A^n+B^n=sum_(j=0)^(|_n/2_|)(-1)^jn/(n-j)(n-j; j)(AB)^j(A+B)^(n-2j), where |_x_| is the floor function and (n; k) is a binomial coefficient.

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be Saalschützian if it is k-balanced with k=1, ...

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

All Mathieu functions have the form e^(irz)f(z), where f(z) has period 2pi and r is known as the Mathieu characteristic exponent. This exponent is returned by the Wolfram ...

A function f which may (but does not necessarily) associate a given member of the range of f with more than one member of the domain of f. For example, trigonometric ...