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The identity _2F_1(x,-x;x+n+1;-1)=(Gamma(x+n+1)Gamma(1/2n+1))/(Gamma(x+1/2n+1)Gamma(n+1)), or equivalently ...
The sequence {F_n-1} is complete even if restricted to subsequences which contain no two consecutive terms, where F_n is a Fibonacci number.
If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...
int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...
Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, then there exists a B_3 in S such ...
Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).
An a×b rectangle can be packed with 1×n strips iff n|a or n|b.
If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...
Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, there exists a B_3 in S such that ...
A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...
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