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The first few terms in the continued fraction of the Champernowne constant are [0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, 45754...10987, 6, 1, 1, 21, ...] ...

A series is said to be conditionally convergent iff it is convergent, the series of its positive terms diverges to positive infinity, and the series of its negative terms ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

There are at least two sequences attributed to B. Recamán. One is the sequence a_n formed by taking a_1=1 and letting a_n={a_(n-1)-n if a_(n-1)-n>0 and is new; a_(n-1)+n ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

Ballantine's series is the series for pi given by pi=864sum_(n=0)^infty((n!)^24^n)/((2n+1)!325^(n+1)) +1824sum_(n=0)^infty((n!)^24^n)/((2n+1)!3250^(n+1))-20cot^(-1)239 ...

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...