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Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

The nested radical constant is the constant defined by C = sqrt(1+sqrt(2+sqrt(3+sqrt(4+sqrt(5+...))))) (1) = 1.75793275... (2) (OEIS A072449). No closed-form expression is ...

The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth ...

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

In number theory (e.g., Ivić 2003), the symbol log_kx is commonly used to mean the nested logarithm (also called the repeated logarithm or iterated logarithm) ...

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...