| 11. | Alternatively, by changing variables, the principal value integral can be written explicitly as:
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| 12. | Its principal value is a poignancy seldom encountered in crime movies.
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| 13. | Thus this formula defines a principal value for arsinh with branch cuts and.
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| 14. | Where \ mathcal { P } denotes the Cauchy principal value.
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| 15. | It can also be defined directly as a principal value integral
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| 16. | It is related to the principal value of the natural logarithm by the formula
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| 17. | Therefore, in the limit, it turns the integral into a Cauchy principal value integral.
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| 18. | Similarly, the principal value will rise when interest rates fall.
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| 19. | And after all the bumps, the principal value goes nowhere.
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| 20. | That, he said, was the principal value of any prize.
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