title: [Increase functions of the type dW/dt = k Wm (E--W)n and their integrals (author's transl)].
abstract: In a preceding paper increase functions have been treated following the Bertalanffy conception of organic growth given in the transformed shape as dW/dt = k Wm (En--Wn). As the growth functions gained by integration reach the final value E only for t leads to infinity, the increase function is changed to dW/dt = k Wm (E--W)n. Now integrations yield growth functions with asymptotic behaviour W leads to E as well as such reaching W = E in finite time, and are so better corresponding with natural development. The mathematical treatment shows a broad variety of resulting integrals given as graphs, some of them having chances as possible growth functions. Future investigations into increase functions should be focussed to the aim of choosing an ansatz allowing allround integrations leading to a variation of the parameters (m and n) in the growth function proper. This would mean avoiding a series of structurally different integrals without continuous transition between them and could be an aggravating mathematical simplification.
mesh_terms: D006128:Growth; D008433:Mathematics; D008962:Models, Theoretical
vernacular_title: Zuwachsfunktionen vom Typ dW/dt = k Wm (E--W)n und ihre Integrale.