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Let phi_x^((k)) denote the recursive function of k variables with Gödel number x, where (1) is normally omitted. Then if g is a partial recursive function, there exists an ...

The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

Ramanujan's Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...

The integral int_0^1x^p(1-x)^qdx, called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

The Fransén-Robinson constant F is defined by F=int_0^infty(dx)/(Gamma(x))=2.8077702420... (OEIS A058655) where Gamma(x) is the gamma function. No closed-form expression in ...

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 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 ...

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, ...