Other versions of several of the identities in this subsection can be
constructed with the aid of the operator identity
See Erdélyi et al. (1953a, pp. 102–103).
The six functions F(a±1,b;c;z), F(a,b±1;c;z),
F(a,b;c±1;z) are said to be contiguous to
By repeated applications of (15.5.11)–(15.5.18) any
function F(a+k,b+ℓ;c+m;z), in which k,ℓ,m are integers, can be
expressed as a linear combination of F(a,b;c;z) and any one of
its contiguous functions, with coefficients that are rational functions of
a,b,c, and z.
An equivalent equation to the hypergeometric differential equation
Further contiguous relations include: