Generalized Harmonic Number

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on

Jun 25, 2021, 2:08:37 PM

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on

Dec 7, 2015, 2:38:47 AM

$H_(n,m) = sum_(k=1)^ "n" 1/k^ "m"$

$(n)"Number of Terms"$

$(m)"Exponent of the Inverse"$

This equation computes the generalized harmonic number of the order n of m:

$H_(n,m) = sum_(k=1)^n 1/(k^m)$

The limit as n tends to infinity exists if m > 1.

If m = 0, $H_(n,0) = n$

If m = 1, $H_(n,1) = H_n = "harmonic number"$ See Harmonic Number.

Other syntactic notations include:

$H_(n,m) = H_n^(m) = H_m(n)$

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