# Can we interpolate Pascal's triangle?

Answer to the title: of course we can interpolate Pascal's triangle with $$z(x,y)= {x \choose y}$$, but my laptop cannot handle the graph of $$z(x,y)$$, and I cannot find one online.

I am looking for high-quality visualizations of the interpolation of Pascal's triangle, particularly for $$x<0$$. Is the triangle still symmetric?

• I took the liberty of adding a plot of $\Gamma(x+y+1)/(\Gamma(x+1)\Gamma(y+1))$, which is the continuous analogue of $\binom{x+y}x=\binom{x+y}y$. Can't avoid the infinities coming from $\Gamma[z]$ having a pole at all the non-positive integer points. This shows in the plot as those spikes and white lines covering points where the function is undefined. Probably marring your viewing pleasure, I'm afraid. – Jyrki Lahtonen Feb 20 at 5:30
• Using the beta-function instead may or may not help a bit. – Jyrki Lahtonen Feb 20 at 5:50