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A number which can be computed to any number of digits desired by a Turing machine. Surprisingly, most irrationals are not computable numbers!

The computational paradigm is a term introduced by Wolfram (2002, 2021) to describe the idea of using simple programs rather than mathematical equations (the latter of which ...

A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the ...

y approx m+sigmaw, (1) where w = (2) where h_1(x) = 1/6He_2(x) (3) h_2(x) = 1/(24)He_3(x) (4) h_(11)(x) = -1/(36)[2He_3(x)+He_1(x)] (5) h_3(x) = 1/(120)He_4(x) (6) h_(12)(x) ...

Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical computation of a univariate integral, and ...

A table made by subtracting adjacent entries in a sequence, then repeating the process with those numbers.

A discriminant is a quantity (usually invariant under certain classes of transformations) which characterizes certain properties of a quantity's roots. The concept of the ...

A fact noticed by physicist G. Gamow when he had an office on the second floor and physicist M. Stern had an office on the sixth floor of a seven-story building (Gamow and ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...