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

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The Generalized Harmonic calculator computes the harmonic number of the order n of m.

INSTRUCTIONS: Enter the following:

• (n) Number of terms
• (m) Exponent of terms

Generalized Harmonic Number (H_m,n): The calculator returns the number as a real.

The Math / Science

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

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

Special cases of the generalized harmonic number

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 notations

Other syntactic notations include:

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