Tables 18.19.1 and 18.19.2 provide definitions via orthogonality and normalization (§§18.2(i), 18.2(iii)) for the Hahn polynomials , Krawtchouk polynomials , Meixner polynomials , and Charlier polynomials .
, | , or | If , then and . | |
, | , | ||
, , | |||
, |
These polynomials are orthogonal on , and with , are defined as follows.
18.19.1 | |||
18.19.2 | |||
18.19.3 | |||
18.19.4 | |||
18.19.5 | |||
These polynomials are orthogonal on , and are defined as follows.
18.19.6 | |||
18.19.7 | |||
18.19.8 | |||
, , | |||
18.19.9 | ||||