| 1. | Where " g " is an arbitrary function for growth rate.
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| 2. | These circuits can be used to compute arbitrary functions of the initial configuration.
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| 3. | Where the are completely arbitrary functions of time.
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| 4. | The Sum function can be employed for arbitrary functions merely by employing the appropriate expressions.
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| 5. | I can factor any arbitrary function of x and y out of any of the terms.
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| 6. | The Hankel transform can express a fairly arbitrary function as an integral of Bessel functions of different scales.
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| 7. | Where \ lambda is an arbitrary complex constant, and U ( \ lambda ) is an arbitrary function.
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| 8. | Note that Z [ J ] as originally defined, is completely independent of the arbitrary function \ chi ( x ).
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| 9. | This is a very practical challenge for algorithms that are meant to find zeros of functions, whether arbitrary functions or simply polynomials.
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| 10. | The skills required to solve a quadratic equation on a calculator are in fact applicable to finding the real roots of any arbitrary function.
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