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HarmonicNumber

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

HarmonicNumber[n]
    gives the n-th harmonic number H_n = Sum_{i=1}^n 1/i.
HarmonicNumber[n, r]
    gives the order-r harmonic number H_n^(r) = Sum_{i=1}^n 1/i^r.
Non-negative integer n expands to the exact finite sum (a rational for
integer r, an explicit sum for symbolic r); HarmonicNumber[Infinity, r] is
Zeta[r]; a non-positive integer order r gives the Faulhaber polynomial in n.
Inexact arguments evaluate numerically at machine or arbitrary (MPFR)
precision, including complex order, via Zeta[r] - Zeta[r, n+1] (and the
digamma form for r = 1). Listable.

Examples

No verified examples yet for this function.

Implementation notes

Attributes: Listable, NumericFunction, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References