# §12.7 Relations to Other Functions

## §12.7(iii) Modified Bessel Functions

For the notation see §10.25(ii).

12.7.8
12.7.9
12.7.10
12.7.11

For these, the corresponding results for with , , , , , and the corresponding results for with , , , , , , , see Miller (1955, pp. 42–43 and 77–79).

## §12.7(iv) Confluent Hypergeometric Functions

For the notation see §§13.2(i) and 13.14(i).

The even and odd solutions of (12.2.2) (see (12.4.3)–(12.4.6)) are given by

12.7.12
12.7.13

Also,

(It should be observed that the functions on the right-hand sides of (12.7.14) are multivalued; hence, for example, cannot be replaced simply by .)