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Binet's first formula for the log gamma function lnGamma(z), where Gamma(z) is a gamma function, is given by for R[z]>0 (Erdélyi et al. 1981, p. 21; Whittaker and Watson ...

The term Borel hierarchy is used to describe a collection of subsets of R defined inductively as follows: Level one consists of all open and closed subsets of R, and upon ...

The function defined by the contour integral J_(n,k)(z) =1/(2pii)int^((0+))t^(-n-1)(t+1/t)^kexp[1/2z(t-1/t)]dt, where int_((0+)) denotes the contour encircling the point z=0 ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...

A real function is said to be differentiable at a point if its derivative exists at that point. The notion of differentiability can also be extended to complex functions ...

If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...

A subset G subset R of the real numbers is said to be a G_delta set provided G is the countable intersection of open sets. The name G_delta comes from German: The G stands ...

Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified ...

An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local ...