Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Proof of the Euler product formula for the Riemann zeta function arithmetic, the partial product when expanded out gives a sum consisting of those terms "n" where "n" is a product of primes less than or equal to "q". The inequality results from the fact that therefore only integers larger than "q" can fail to appear in this expanded out partial product. Since the difference between the partial product and ζ("s") goes to zero when σ > 1, we have convergence in this region. Proof of the Euler product formula for the Riemann zeta function Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis "Variae