Central and local limit theorems for the weighted Delannoy numbers

Abstract

In this research we generalize our result for numbers satisfying the Delannoy triangle. We obtain a central limit theorem and a local limit theorem for weighted numbers of the triangle and establish the rate of convergence to the limiting (normal) distribution.

Keywords

• delannoy triangle
• central limit theorem
• local limit theorem
• double generating function
• triangular array
• primary 05a15
• 05a16
• 60f05
• secondary 39a06
• 39a14