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1: 16.6 Transformations of Variable
16.6.2 F 2 3 ( a , 2 b - a - 1 , 2 - 2 b + a b , a - b + 3 2 ; z 4 ) = ( 1 - z ) - a F 2 3 ( 1 3 a , 1 3 a + 1 3 , 1 3 a + 2 3 b , a - b + 3 2 ; - 27 z 4 ( 1 - z ) 3 ) .
For Kummer-type transformations of F 2 2 functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).
2: 13.10 Integrals
§13.10(ii) Laplace Transforms
§13.10(iii) Mellin Transforms
§13.10(iv) Fourier Transforms
§13.10(v) Hankel Transforms
3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
Kummer Transformation
4: 13.2 Definitions and Basic Properties
Kummer’s Transformations
5: Bibliography P
  • R. B. Paris (2005a) A Kummer-type transformation for a F 2 2 hypergeometric function. J. Comput. Appl. Math. 173 (2), pp. 379–382.
  • 6: 13.9 Zeros
    §13.9(i) Zeros of M ( a , b , z )
    §13.9(ii) Zeros of U ( a , b , z )
    7: 16.4 Argument Unity
    §16.4(iii) Identities
    8: 33.14 Definitions and Basic Properties
    This is a consequence of Kummer’s transformation13.2(vii)). …
    9: 33.2 Definitions and Basic Properties
    This is a consequence of Kummer’s transformation13.2(vii)). …
    10: 13.8 Asymptotic Approximations for Large Parameters
    When the foregoing results are combined with Kummer’s transformation (13.2.39), an approximation is obtained for the case when | b | is large, and | b - a | and | z | are bounded. …