Digital Library of Mathematical Functions
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15 Hypergeometric FunctionProperties

§15.7 Continued Fractions

If |ph(1-z)|<π, then

15.7.1 F(a,b;c;z)F(a,b+1;c+1;z)=t0-u1zt1-u2zt2-u3zt3-,

where

15.7.2 tn =c+n,
u2n+1 =(a+n)(c-b+n),
u2n =(b+n)(c-a+n).

See also Cuyt et al. (2008, pp. 295–309).