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.
- Confluent Hypergeometric Function of the First Kind
- Confluent Hypergeometric Function of the Second Kind
- Confluent Hypergeometric Limit Function
- Confocal Conics
- Confocal Ellipsoidal Coordinates
- Confocal Parabolic Coordinates
- Confocal Paraboloidal Coordinates
- Conformal Latitude
- Conformal Map
- Conformal Solution
- Conformal Tensor
- Conformal Transformation
- Congruence
- Congruence Axioms
- Congruence (Geometric)
- Congruence Transformation
- Congruent
- Congruent Incircles Point
- Congruent Isoscelizers Point
- Congruent Numbers
- Congruum
- Congruum Problem
- Conic
- Conical Coordinates
- Conical Frustum