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5 Gamma FunctionProperties

§5.10 Continued Fractions

For z>0,

5.10.1 lnΓ(z)+z-(z-12)lnz-12ln(2π)=a0z+a1z+a2z+a3z+a4z+a5z+,

where

5.10.2 a0 =112,
a1 =130,
a2 =53210,
a3 =195371,
a4 =2299922737,
a5 =299 44523197 33142,
a6 =10 95352 410094 82642 75462.

For exact values of a7 to a11 and 40S values of a0 to a40, see Char (1980). Also see Cuyt et al. (2008, pp. 223–228), Jones and Thron (1980, pp. 348–350), Lorentzen and Waadeland (1992, pp. 221–224), and Mortici (2011a) for further information.