<sod>  
 :<math>{r \choose k}=\frac{(-1)^k}{k!}(-r)_k,</math>
 
which is important when one is working with infinite series and would like to represent them in terms of [[generalized hypergeometric function]]s. The notation <math>(\cdot)_k</math> represents the [[Pochhammer symbol]]. This form is vital in applied mathematics, for example, when evaluating the formulas that model the statistical properties of the phase-front curvature of a light wave as it propagates through optical atmospheric turbulence. 
 
 A particularly handy but non-obvious form holds for the reciprocal power: 
 :<math>\frac{1}{(1-x)^r}=\sum_{k=0}^\infty {r+k-1 \choose k} x^k \equiv \sum_{k=0}^\infty {r+k-1 \choose r-1} x^k.</math>
 <eod> <sod> 
 :<math>{r \choose k}=\frac{(-1)^k}{k!}(-r)_k,</math>
 
which is important when one is working with infinite series and would like to represent them in terms of [[generalized hypergeometric function]]s. The notation <math>(\cdot)_k</math> is the [[Pochhammer symbol]]. This form is vital in applied mathematics, for example, when evaluating the formulas that model the statistical properties of the phase-front curvature of a light wave as it propagates through optical atmospheric turbulence. 
 
 A particularly handy but non-obvious form holds for the reciprocal power: 
 :<math>\frac{1}{(1-x)^r}=\sum_{k=0}^\infty {r+k-1 \choose k} x^k \equiv \sum_{k=0}^\infty {r+k-1 \choose r-1} x^k.</math>
 <eod>