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1: DLMF Project News
error generating summary2: 15.20 Software
3: 35.10 Methods of Computation
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βΊSee Yan (1992) for the and functions of matrix argument in the case , and Bingham et al. (1992) for Monte Carlo simulation on applied to a generalization of the integral (35.5.8).
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4: 15.4 Special Cases
5: 4.29 Graphics
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βΊ
§4.29(i) Real Arguments
… βΊ … βΊ βΊ§4.29(ii) Complex Arguments
βΊThe conformal mapping is obtainable from Figure 4.15.7 by rotating both the -plane and the -plane through an angle , compare (4.28.8). …6: 35.7 Gaussian Hypergeometric Function of Matrix Argument
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βΊ
35.7.1
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βΊ
35.7.2
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βΊ
35.7.3
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βΊLet (a) be orthogonally invariant, so that is a symmetric function of , the eigenvalues of the matrix argument
; (b) be analytic in in a neighborhood of ; (c) satisfy .
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βΊSystems of partial differential equations for the (defined in §35.8) and functions of matrix argument can be obtained by applying (35.8.9) and (35.8.10) to (35.7.9).
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7: 35.8 Generalized Hypergeometric Functions of Matrix Argument
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βΊThe generalized hypergeometric function with matrix argument
, numerator parameters , and denominator parameters is
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βΊ
35.8.4
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βΊ
35.8.8
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βΊMultidimensional Mellin–Barnes integrals are established in Ding et al. (1996) for the functions and of matrix argument.
A similar result for the function of matrix argument is given in Faraut and Korányi (1994, p. 346).
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8: 35.6 Confluent Hypergeometric Functions of Matrix Argument
9: 14.2 Differential Equations
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βΊUnless stated otherwise in §§14.2–14.20 it is assumed that the arguments of the functions and lie in the interval , and the arguments of the functions , , and lie in the interval .
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