| 21. | Replacing by gives the moment generating function of.
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| 22. | This umbral exponential thus amounts to the exponential generating function of the Pochhammer symbols.
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| 23. | Since the generating function for a ^ n is
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| 24. | And is clearly very closely related to the cumulant generating function for the energy.
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| 25. | The ordinary generating function for the sequences are:
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| 26. | Clearly the orbits do not intersect and we may add the respective generating functions.
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| 27. | Then the "'Whitney rank generating function "'is defined as
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| 28. | Once determined, the generating function yields the information given by the previous approaches.
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| 29. | These latter names come from the study of the generating function for the sequence.
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| 30. | In the above example, the function divisor generates functions with a specified divisor.
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