CAOP

Plot

Charlier Polynomials

Definition

The Charlier polynomials are defined as

\[ \begin{align} C_n(x,a) &= \sum_{k=0}^n {n \choose k} {x \choose k} k! \left(-\frac{1}{a}\right)^k\\ &= {}_2F_0 \left(\left. {-n, -x \atop -} \; \right| -\frac{1}{a} \right) \end{align} \]

Difference Equation

Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

Parameters

\(a\) \(a > 0\)

factor (use Maple-style input)

   hypergeometric term in \(n\) and hypergeometric term in \(x\) required