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