Definition.
Orthogonality.
Recurrence relation.
Normalized recurrence relation.
where
Difference equation.
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
Rodrigues-type formula.
Generating functions.
Remarks. The Meixner polynomials defined by (1.9.1) and the Jacobi polynomials given by (1.8.1) are related in the following way :
The Meixner polynomials are also related to the Krawtchouk polynomials defined by (1.10.1) in the following way :
References. [6], [10], [13], [19], [21], [31], [32], [39], [43], [50], [52], [64], [67], [69], [80], [104], [123], [130], [154], [170], [172], [173], [181], [183], [212], [222], [227], [233], [239], [247], [250], [274], [286], [287], [296], [298], [301], [307], [316], [323], [338], [391], [394], [407], [409].
