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16 Generalized Hypergeometric Functions & Meijer G-FunctionGeneralized Hypergeometric Functions

Β§16.6 Transformations of Variable


16.6.1 F23⁑(a,b,caβˆ’b+1,aβˆ’c+1;z)=(1βˆ’z)βˆ’a⁒F23⁑(aβˆ’bβˆ’c+1,12⁒a,12⁒(a+1)aβˆ’b+1,aβˆ’c+1;βˆ’4⁒z(1βˆ’z)2).


16.6.2 F23⁑(a,2⁒bβˆ’aβˆ’1,2βˆ’2⁒b+ab,aβˆ’b+32;z4)=(1βˆ’z)βˆ’a⁒F23⁑(13⁒a,13⁒a+13,13⁒a+23b,aβˆ’b+32;βˆ’27⁒z4⁒(1βˆ’z)3).

For Kummer-type transformations of F22 functions see Miller (2003) and Paris (2005a), and for further transformations see ErdΓ©lyi et al. (1953a, Β§4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).