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Harmonic Expansion

A harmonic series is a continued fraction-like series [n;a,b,c,...] defined by

x=n+1/2(a+1/3(b+1/4(c+...)))

(Havil 2003, p. 99).

Examples are given in the following table.

cOEISharmonic expansion
eA054977[2, 1, 1, 1, 1, 1, 1, ...]
gammaA096622[0, 1, 0, 1, 4, 1, 4, ...]
piA075874[3, 0, 0, 3, 1, 5, 6, 5, ...]

See also

Continued Fraction, Engel Expansion, Harmonic Series

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References

Havil, J. "Harmonic Expansion." §11.8 in Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 98-100, 2003.Sloane, N. J. A. Sequences A054977, A075874, and A096622 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Harmonic Expansion

Cite this as:

Weisstein, Eric W. "Harmonic Expansion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HarmonicExpansion.html

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