Logarithmic Binomial Theorem
For all integers 
and 
,
where
is the Harmonic Logarithm and 
is a Roman Coefficient. For
, the logarithmic binomial theorem reduces to the classical Binomial Theorem for Positive , since
for 
, 
for 
, and 
when 
.Similarly, taking 
and 
gives theNegative Binomial Series. Roman (1992) gives expressions obtained for the case and 
which are notobtainable from the Binomial Theorem.
References
Roman, S. ``The Logarithmic Binomial Formula.'' Amer. Math. Monthly 99, 641-648, 1992.
- Interspersion
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