Basic Examples (2) 

Convert an ordinary harmonic number to an inactive finite sum:

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Convert an alternating harmonic number:

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Scope (9) 

Convert a generalized harmonic number with symbolic order r:

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Include an additional color or scale parameter s in the generalized harmonic number:

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Convert a higher-order alternating harmonic number:

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Combine the alternating sign with a symbolic order and color parameter:

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For first-order hyperharmonic numbers, the result is the corresponding generalized harmonic sum:

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For higher-order hyperharmonic numbers, the function writes the result as a sum over a lower-order hyperharmonic number:

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MultipleHarmonicNumber[n] reduces to the same one-dimensional sum as the ordinary harmonic number:

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A depth-two multiple harmonic number becomes a nested sum with a strict upper bound for the inner index:

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Color parameters in a multiple harmonic number are carried into the nested summand:

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