# §33.13 Complex Variable and Parameters

The functions , , and may be extended to noninteger values of by generalizing , and supplementing (33.6.5) by a formula derived from (33.2.8) with expanded via (13.2.42).

These functions may also be continued analytically to complex values of , , and . The quantities , , and , given by (33.2.6), (33.2.10), and (33.4.1), respectively, must be defined consistently so that

and

For further information see Dzieciol et al. (1999), Thompson and Barnett (1986), and Humblet (1984).