| 21. | These latter names come from the study of the generating function for the sequence.
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| 22. | This umbral exponential thus amounts to the exponential generating function of the Pochhammer symbols.
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| 23. | The sum of this infinite series is the generating function.
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| 24. | In your case, using generating functions seems a reasonable way for treating the sums.
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| 25. | And is clearly very closely related to the cumulant generating function for the energy.
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| 26. | Clearly the orbits do not intersect and we may add the respective generating functions.
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| 27. | So, let's try to find the solution using generating functions.
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| 28. | Since the generating function for a ^ n is
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| 29. | Similar asymptotic analysis is possible for exponential generating functions.
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| 30. | Expressions for the ordinary generating function of other sequences are easily derived from this one.
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