Digital Library of Mathematical Functions
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16 Generalized Hypergeometric Functions and Meijer G-FunctionGeneralized Hypergeometric Functions

§16.6 Transformations of Variable

Quadratic

16.6.1 F23(a,b,ca-b+1,a-c+1;z)=(1-z)-aF23(a-b-c+1,12a,12(a+1)a-b+1,a-c+1;-4z(1-z)2).

Cubic

16.6.2 F23(a,2b-a-1,2-2b+ab,a-b+32;z4)=(1-z)-aF23(13a,13a+13,13a+23b,a-b+32;-27z4(1-z)3).

For Kummer-type transformations of F22 functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5) and Miller and Paris (2011).