| 1. | The process can be analyzed using the method of probability generating function.
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| 2. | Two random variables having equal moment generating functions have the same distribution.
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| 3. | The ordinary generating function can be generalized to arrays with multiple indices.
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| 4. | This representation is unique : different multisets have different cumulant generating functions.
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| 5. | In the above example, the function divisor generates functions with a specified divisor.
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| 6. | The generating function of the coefficients a _ n is then
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| 7. | The resulting series is the generating function for the Legendre polynomials:
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| 8. | Once determined, the generating function yields the information given by the previous approaches.
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| 9. | The result is that all generating functions involved have the form
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| 10. | One is based on analytical calculations by using generating function techniques.
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