Difference between revisions of "Relationship between Meixner polynomials and Charlier polynomials"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula hold...") |
|||
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\lim_{\beta \rightarrow \infty} M_n \left(x;\beta,\dfrac{a}{\beta+a} \right) = C_n(x;a),$$ | $$\displaystyle\lim_{\beta \rightarrow \infty} M_n \left(x;\beta,\dfrac{a}{\beta+a} \right) = C_n(x;a),$$ | ||
where $M_n$ denotes a [[Meixner polynomial]] and $C_n$ denotes a [[Charlier polynomial]]. | where $M_n$ denotes a [[Meixner polynomial]] and $C_n$ denotes a [[Charlier polynomial]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 02:40, 21 December 2016
Theorem
The following formula holds: $$\displaystyle\lim_{\beta \rightarrow \infty} M_n \left(x;\beta,\dfrac{a}{\beta+a} \right) = C_n(x;a),$$ where $M_n$ denotes a Meixner polynomial and $C_n$ denotes a Charlier polynomial.
