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I want to show

$$ \left( \begin{array}{ccccc} &1 &\wp(v) &\wp'(v) \\ &1 &\wp(w) &\wp'(w) \\ &1 &\wp(v+w) &-\wp'(v+w) \end{array} \right)=0 $$

where $\wp$ denotes the Weierstrass elliptic function.

  • 2
    You might find [this thread](http://math.stackexchange.com/q/52021/5363) useful.2012-03-18
  • 1
    In particular, look at Bruno's answer. Your determinant vanishing is equivalent to the fact that $(P(v), P'(v))$, $(P(w), P'(w))$ and $(-P(v+w), -P'(v+w))$ are colinear, which is shown in the last paragraph of Bruno's answer.2012-03-18

1 Answers 1