title: [Increase functions of the type dW/dt = ktp-1(tEp--tp)q and their integrals (author's transl)].
abstract: After the investigations into 4 increase functions of organic growth a fifth ansatz should be added as dW/dt = ktp(tE--t)q with only the time t involved on the right side of the equation. In the course of researches about approximations the author has dealed with this type of functions, which can only be integrated within the limits t = 0 and t = tE leading to the Beta-function with W = E as a restricted result. Therefore the basic equation was thoroughly modified as to fit the type dW/dt = cf(t) df(t)/dt. Surprisingly the integration results in a growth function formally equal to the solution for the increase function dW/dt = ktp(E--W)n. Although the determination of the coefficients runs along other lines, the traditional example given in the preceding papers shows values so close to each other as to suppose genuine identity, which is finally proved. The fact, that seemingly quite different increase functions can lead to identical results must be given serious account: judging about increase functions should be taken as a rather delicate matter.
mesh_terms: D000818:Animals; D006128:Growth; D006801:Humans; D008433:Mathematics
vernacular_title: Zuwachsfunktionen vom Typ dW/dt = ktp-1(tEp--tp)q und ihre Integrale.