# §24.14 Sums

###### Contents

Let be even with and nonzero. Then

## §24.14(ii) Higher-Order Recurrence Relations

In the following two identities, valid for , the sums are taken over all nonnegative integers with .

In the next identity, valid for , the sum is taken over all positive integers with .

For (24.14.11) and (24.14.12), see Al-Salam and Carlitz (1959). These identities can be regarded as higher-order recurrences. Let denote a Hankel (or persymmetric) determinant, that is, an determinant with element in row and column for . Then