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Line 45: ==The parameter <math>\alpha</math>== In many publications the parameter <math>\alpha</math> is omitted. Also, in different publications different values of <math>\alpha</math> are being implicitly assumed. For example, in the theory of real random matrices (see, e.g., Muirhead, 1984), <math>\alpha=2</math> whereas in other settings (e.g., in the complex ~~case--see~~case—see Gross and Richards, 1989), <math>\alpha=1</math>. To make matters worse, in random matrix theory researchers tend to prefer a parameter called <math>\beta</math> instead of <math>\alpha</math> which is used in combinatorics. The thing to remember is that Line 58: * K. I. Gross and D. St. P. Richards, "Total positivity, spherical series, and hypergeometric functions of matrix argument", ''J. Approx. Theory'', '''59''', no. 2, 224–246, 1989. * J. Kaneko, "Selberg Integrals and hypergeometric functions associated with Jack polynomials", ''SIAM Journal on Mathematical Analysis'', '''24''', no. 4, 1086-1110, 1993. * Plamen Koev and Alan Edelman, "The efficient evaluation of the hypergeometric function of a matrix argument", ''Mathematics of Computation'', '''75''', no. 254, 833-846, 2006. * Robb Muirhead, ''Aspects of Multivariate Statistical Theory'', John Wiley & Sons, Inc., New York, 1984. ==External links== * [http://www-math.mit.edu/~plamen/software/mhgref.html Software for computing the hypergeometric function of a matrix argument] by Plamen Koev.

Hypergeometric function of a matrix argument: Difference between revisions