21. The two-parameter generalization of the original Yule distribution replaces the beta function with an incomplete beta function . 22. The use of the incomplete beta function has the effect of introducing an exponential cutoff in the upper tail. 23. For proving the correctness of the above definition of the \ beta function , we shall use several lemmas. 24. The beta function , \ Beta, is a normalization constant to ensure that the total probability integrates to 1. 25. The one-loop beta function in quantum chromodynamics with n _ f flavours and n _ s scalar Higgs bosons is 26. Note that non-perturbative processes may correct this, for example through contributions to the beta functions due to instantons. 27. Euler integral of the second kind "'( the Euler integral of the first kind defines the beta function ). 28. Perturbation theory permits to evaluate beta function in this limit producing the following result for SU ( " N ") 29. This beta function tells us that the coupling increases with increasing energy scale, and QED becomes strongly coupled at high energy. 30. Caswell did work in quantum gauge theory, most notably, his 1972 calculation of the beta function to two-loop accuracy.
