11. It can also be represented in terms of the regularized incomplete beta function , as follows: 12. Now we introduce the beta function . 13. First, the one instanton correction was calculated by Nathan Seiberg in Supersymmetry and Nonperturbative beta Functions . 14. G�del defined the \ beta function using the Chinese remainder theorem in his article written in 1931. 15. The full nonperturbative proof by Nathan Seiberg appeared in the 1988 article Supersymmetry and Nonperturbative beta Functions . 16. Where B ( ) is the Beta function and \ Gamma ( ) is the Gamma function. 17. In the opposite limit of low energies ( infrared limit ), the beta function is not known. 18. An example is quantum electrodynamics ( QED ), where one finds by using beta function is positive. 19. In this case, the non-zero beta function tells us that the classical scale invariance is anomalous. 20. The two-parameter generalization of the original Yule distribution replaces the beta function with an incomplete beta function.
