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1: 17.11 Transformations of -Appell Functions
2: 27.3 Multiplicative Properties
§27.3 Multiplicative Properties
… βΊIf is multiplicative, then the values for are determined by the values at the prime powers. …Related multiplicative properties are … βΊA function is completely multiplicative if and … βΊIf is completely multiplicative, then (27.3.2) becomes …3: 17.7 Special Cases of Higher Functions
4: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
5: 17.10 Transformations of Functions
6: 17.8 Special Cases of Functions
7: 17.9 Further Transformations of Functions
8: 27.20 Methods of Computation: Other Number-Theoretic Functions
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βΊTo calculate a multiplicative function it suffices to determine its values at the prime powers and then use (27.3.2).
For a completely multiplicative function we use the values at the primes together with (27.3.10).
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9: 17.6 Function
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βΊ
17.6.1
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βΊ
17.6.5
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βΊ
17.6.13
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βΊ
17.6.29
βΊwhere , , and the contour of integration separates the poles of from those of , and the infimum of the distances of the poles from the contour is positive.
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