Power Series Expansion for Reciprocal of 1-z to the m+1 by Logarithm of Reciprocal of 1-z

Theorem

 * $\dfrac 1 {\paren {1 - z}^{m + 1} } \map \ln {\dfrac 1 {1 - z} } = \ds \sum_{k \mathop \ge 1} \paren {H_{m + k} - H_m} \dbinom {m + k} k z^k$

where:
 * $\dbinom {m + k} k$ denotes a binomial coefficient
 * $H_m$ denotes the $m$th harmonic number.