Show that Hint: use Weierstrass product formula
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Originally Posted by EinStone Show that Hint: use Weierstrass product formula Now take 's of both sides. Now differentiate both sides. This process is called logarithmic differentiation.
Oh nice it was easy, somehow I havent heard that term before. Here yet another problem: Show that, for real z > 0, we have as
Originally Posted by EinStone Oh nice it was easy, somehow I havent heard that term before. Here yet another problem: Show that, for real z > 0, we have as since the previous sum is telescoping. Now it's a well known fact that for and , . (Ask if you'd like to see why.) Thus as . (I omitted the absolute value since .)
Ok thanks, could you say something about the log x thing? A reference is enough or just give the general idea, I dont need details.
Originally Posted by EinStone Ok thanks, could you say something about the log x thing? A reference is enough or just give the general idea, I dont need details. Perform LRAM and RRAM with step size to approximate , where . We know that , but since is monotonically decreasing, RRAM LRAM. Now RRAM LRAM Another way to prove this is by applying the Euler Maclaurin formula to , if you are familiar.
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