Zur Theorie der Gammafunction

Ohne Zusammenfassung Vergl. meine Abhandlung:Om en ny klass af transcendenta functioner, hvilka ?ro n?ra besl?gtade med gammafunktionen, Acta soc. scient. Fennic?, Tom. XIV, XV; 1885, 1886.     

Auf die mannigfache Verwendbarkeit der Centrifugalmaschine zu analytischen Zwecken

Ohne Zusammenfassung     

On Nuclear Reaction Rate Theory

A fundamental problem in the theory of cosmological and stellar nucleosynthesis is the determination of reaction rates. The current theories of nuclear kinetics are equilibrium theories with a strict Maxwell-Boltzmannian approach to the evaluation of reaction rates. This paper investigates in some detail the relation between the macroscopic nuclear reaction probability and the microscopic nuclear reaction cross section on the basis of equilibrium-thermodynamic arguments. A general form of the nuclear reaction probability is derived, and the most general collision probability integral is evaluated in closed form for all convenient values of the parameters by using random variables.     

Analytic Representations of Thermonuclear Reaction Rates

The basic physical principles common to all nonresonant and resonant thermonuclear reaction rates are taken as a basis to derive the standard forms of both types of reaction rates. Results are given for the closed-form representations of the standard nonresonant and resonant thermonuclear reaction rates in terms of a certain type of Meijer's G-function. Then, for physical reasons the nonresonant reaction rate with modified Maxwell-Boltzmann distribution is considered. The mathematical method for the derivation of closed-form representations for the modified nonresonant reaction-rate integral, which is also suitable for numerical computations, is given in detail. Some new techniques developed by the authors are used for deriving the results. The reaction-rate systematics thus obtained in terms of Meijer's G-function is a contribution to Fowler's methods for the numerical computation of thermonuclear reaction rates.