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.
- Right Hyperbola
- Right Line
- Right Strophoid
- Right Strophoid Inverse Curve
- Right Triangle
- Rigid
- Rigidity Theorem
- Rigid Motion
- Ring
- Ring Cyclide
- Ring Function
- Ringoid
- Ring Torus
- Risch Algorithm
- Rising Factorial
- Rivest-Shamir-Adleman Number
- RMS
- r(n)
- Robbin Constant
- Robbins Algebra
- Robbins Equation
- Robbin's Inequality
- Robertson Condition
- Robertson Conjecture
- Robertson-Seymour Theorem