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The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

A fractal produced by iteration of the equation z_(n+1)=z_n^2 (mod m) which results in a Moiré-like pattern.

((a+b)/2)^2-((a-b)/2)^2=ab.

A regression that is linear in the unknown parameters used in the fit. The most common form of linear regression is least squares fitting. Least squares fitting of lines and ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

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) = ...

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

An fairly good numerical integration technique. The method is also available in the Wolfram Language using the option Method -> DoubleExponential to NIntegrate.

An exponential generating function for the integer sequence a_0, a_1, ... is a function E(x) such that E(x) = sum_(k=0)^(infty)a_k(x^k)/(k!) (1) = ...

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...