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The vercosine, written vercos(z) and also known as the "versed cosine," is a little-used trigonometric function defined by vercos(z) = 2cos^2(1/2z) (1) = 1+cosz, (2) where ...

The entire function phi(rho,beta;z)=sum_(k=0)^infty(z^k)/(k!Gamma(rhok+beta)), where rho>-1 and beta in C, named after the British mathematician E. M. Wright.

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 ...

The zeta Fuchsians are class of functions discovered by Poincaré which are related to the automorphic functions.

Let z=x+iy and f(z)=u(x,y)+iv(x,y) on some region G containing the point z_0. If f(z) satisfies the Cauchy-Riemann equations and has continuous first partial derivatives in ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

Let mu be a positive measure on a sigma-algebra M, and let lambda be an arbitrary (real or complex) measure on M. If there is a set A in M such that lambda(E)=lambda(A ...

Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).