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The Yiu circle is the circumcircle of the Yiu triangle DeltaO_AO_BO_C. It has center function given by alpha=af(a,b,c), where f(a,b,c) is a 14th-order polynomial. Its radius ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

The Riemann-Siegel formula is a formula discovered (but not published) by Riemann for computing an asymptotic formula for the Riemann-Siegel function theta(t). The formula ...

A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

The case of the Weierstrass elliptic function with invariants g_2=0 and g_3=1. The corresponding real half-period is given by omega_2 = (Gamma^3(1/3))/(4pi) (1) = ...

The second-order ordinary differential equation y^('')+2xy^'-2ny=0, (1) whose solutions may be written either y=Aerfc_n(x)+Berfc_n(-x), (2) where erfc_n(x) is the repeated ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

Euler (1738, 1753) considered the series s_a(x)=sum_(n=1)^infty[1/(1-a^n)product_(k=0)^(n-1)(1-xa^(-k))]. He showed that just like log_a(a^n)=n, s_a(a^n)=n for nonnegative ...