Roman Factorial

 |_n]!={n!   for n>=0; ((-1)^(-n-1))/((-n-1)!)   for n<0.

The Roman factorial arises in the definition of the harmonic logarithm and Roman coefficient. It obeys the identities



 |_n]={n   for n!=0; 1   for n=0


 n<0={1   for n<0; 0   for n>=0.

See also

Harmonic Logarithm, Harmonic Number, Roman Coefficient

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Loeb, D. E. "A Generalization of the Binomial Coefficients." 9 Feb 1995., D. and Rota, G.-C. "Formal Power Series of Logarithmic Type." Advances Math. 75, 1-118, 1989.Roman, S. "The Logarithmic Binomial Formula." Amer. Math. Monthly 99, 641-648, 1992.

Referenced on Wolfram|Alpha

Roman Factorial

Cite this as:

Weisstein, Eric W. "Roman Factorial." From MathWorld--A Wolfram Web Resource.

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