Digital Library of Mathematical Functions
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8 Incomplete Gamma and Related FunctionsIncomplete Gamma Functions

§8.9 Continued Fractions

8.9.1 Γ(a+1)zγ*(a,z) =11-za+1+za+2-(a+1)za+3+2za+4-(a+2)za+5+3za+6-,
a-1,-2,,
8.9.2 z-azΓ(a,z) =z-11+(1-a)z-11+z-11+(2-a)z-11+2z-11+(3-a)z-11+3z-11+,
|phz|<π.

For these expansions and further information see Jones and Thron (1985). See also Cuyt et al. (2008, pp. 240–251).