In the theory of trigonometric functions, the following identity is known $$ \sin(u) + \sin(v)=2\sin \left( \frac{u+v}{2} \right) \cos \left( \frac{u-v}{2} \right) $$
There are other, similar-looking identities, known as the sum-to-product identities.
Are there similar identities involving the Weierstrass elliptic functions, $\wp$ and $\wp^\prime$? More specifically, are there identities simplifying the expressions below? $$\wp(u;g_2,g_3) \pm \wp(v;g_2,g_3) \qquad\qquad\wp'(u;g_2,g_3) \pm \wp'(v;g_2,g_3)$$
Thank you!