17.6.1 | |||
17.6.2 | |||
This reverses the order of summation in (17.6.2):
17.6.3 | |||
For similar formulas see Verma and Jain (1983).
17.6.5 | |||
. | |||
17.6.6 | |||
. | |||
17.6.7 | |||
. | |||
17.6.8 | |||
. | |||
17.6.9 | |||
. | |||
17.6.10 | |||
. | |||
17.6.11 | |||
. | |||
17.6.12 | |||
. | |||
17.6.13 | |||
17.6.14 | |||
17.6.15 | |||
. | |||
17.6.16 | |||
, . | |||
For a similar result for -confluent hypergeometric functions see Morita (2013).
17.6.17 | ||||
17.6.18 | ||||
17.6.19 | ||||
17.6.20 | ||||
17.6.21 | ||||
17.6.22 | ||||
17.6.23 | |||
17.6.24 | |||
17.6.25 | ||||
17.6.26 | ||||
17.6.27 | |||
17.6.28 | ||||
17.6.29 | ||||
where , , and the contour of integration separates the poles of from those of , and the infimum of the distances of the poles from the contour is positive.
For continued-fraction representations of the function, see Cuyt et al. (2008, pp. 395–399).