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1: 16.6 Transformations of Variable
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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 ) .
β–ΊFor 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
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§13.10(ii) Laplace Transforms
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§13.10(iii) Mellin Transforms
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§13.10(iv) Fourier Transforms
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§13.10(v) Hankel Transforms
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3: 35.8 Generalized Hypergeometric Functions of Matrix Argument
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Kummer Transformation
4: 13.2 Definitions and Basic Properties
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Kummer’s Transformations
5: Bibliography P
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  • 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
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    §13.9(i) Zeros of M ⁑ ( a , b , z )
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    §13.9(ii) Zeros of U ⁑ ( a , b , z )
    7: 16.4 Argument Unity
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    §16.4(iii) Identities
    8: 33.14 Definitions and Basic Properties
    β–ΊThis is a consequence of Kummer’s transformation13.2(vii)). …
    9: 33.2 Definitions and Basic Properties
    β–ΊThis is a consequence of Kummer’s transformation13.2(vii)). …
    10: 13.8 Asymptotic Approximations for Large Parameters
    β–ΊWhen 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. …