chapter 5

1 Classification

Pages 3

II. Not of type I, but the quotients (5.2) are rational functions of k. A typical example is the binomial formula (7.1),

( n

k

) zk = (1 + z)n,

with quotient equal to

q(z, n, k) = n− k −1− k (−z).

III. Not of type I or II, but the terms are products or quotients of terms which are of type I or II by factors or divisors of the form [x + ky]k, where 0 = y = ±1. A typical example is the Hagen-Rothe formula (13.5),

( n

k

) [x + kz − 1]k−1[y + (n− k)z − 1]n−k−1

= x + y xy

[x + y + nz − 1]n−1.