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We derive the analytical solutions to the second order generalisedgravi-proprioceptive equation given in our recent paper [Bastien et al. 2012].These equations show how plants adjust to the surrounding gravitation field andhighlight the fact that the plant must be able to not only sense its localposture with respect to the gravitational field, but also to sense its ownlocal curvature. In [Bastien et al. 2012] we obtained explicit analyticalsolutions of these equations in terms of (sums of) Bessel functions, and in thepresent paper we derive these solutions.

Analytical Solution of the Proprio-Graviceptive equation for shoot gravitropism of plants