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For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...

A pair of numbers m and n such that sigma(m)=sigma(n)=m+n-1, where sigma(m) is the divisor function. Beck and Najar (1977) found 11 augmented amicable pairs.

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

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

Another "beta function" defined in terms of an integral is the "exponential" beta function, given by beta_n(z) = int_(-1)^1t^ne^(-zt)dt (1) = ...

Involving two variables, as opposed to many (multivariate), or one (univariate).

A generalization of Schröter's formula.

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

When n is an integer >=0, then J_n(z) and J_(n+m)(z) have no common zeros other than at z=0 for m an integer >=1, where J_n(z) is a Bessel function of the first kind. The ...