(41) Γ(x+1) [HP-41C]

[Albert Chan]

We can easily get reciprocal of continued fraction (here, b is rest of the CF terms).

\(\large 1 ÷ \left( 1 + \Large {1 \over (a-{1\over2})\;+\;b\;} \right)
= \frac{(a-{1\over2})\;+\;b}{(a+{1\over2})\;+\;b}
= \large 1 - \Large {1 \over (a+{1\over2})\;+\;b\;}
\)

Example, this is the code for 1/Γ(x), using correction 1/c3(x)

Code:

50 DEF FNR(X)                              ! = 1/gamma
60 C=1 @ WHILE X<12 @ C=C*X @ X=X+1 @ END WHILE
70 C=C/(SQRT(2*PI)*X^(X-.5)*EXP(-X))       ! 1/stirling
80 FNR=C-C/(12*X+.5+1/(720/293*X+.609/X))  ! correction
90 END DEF