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1: 35.8 Generalized Hypergeometric Functions of Matrix Argument
Convergence Properties
§35.8(iv) General Properties
2: 16.2 Definition and Analytic Properties
§16.2(ii) Case p q
§16.2(iii) Case p = q + 1
§16.2(iv) Case p > q + 1
§16.2(v) Behavior with Respect to Parameters
3: Bibliography R
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.
  • 4: 16.5 Integral Representations and Integrals
    where the contour of integration separates the poles of Γ ( a k + s ) , k = 1 , , p , from those of Γ ( - s ) . …
    5: 1.15 Summability Methods
    General Cesàro Summability
    and satisfies the property
    6: 25.16 Mathematical Applications
    For further properties of H ( s , z ) see Apostol and Vu (1984). …
    7: 9.13 Generalized Airy Functions
    Properties of A n ( z ) and B n ( z ) follow from the corresponding properties of the modified Bessel functions. … The distribution in and asymptotic properties of the zeros of A n ( z ) , A n ( z ) , B n ( z ) , and B n ( z ) are investigated in Swanson and Headley (1967) and Headley and Barwell (1975). …
    8: 18.5 Explicit Representations
    18.5.5 p n ( x ) = 1 κ n w ( x ) d n d x n ( w ( x ) ( F ( x ) ) n ) .
    9: Bibliography G
  • I. M. Gel’fand and G. E. Shilov (1964) Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.
  • Z. Gong, L. Zejda, W. Dappen, and J. M. Aparicio (2001) Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.
  • 10: 14.29 Generalizations
    §14.29 Generalizations
    are called Generalized Associated Legendre Functions. …For properties see Virchenko and Fedotova (2001) and Braaksma and Meulenbeld (1967). For inhomogeneous versions of the associated Legendre equation, and properties of their solutions, see Babister (1967, pp. 252–264).