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m Remove blank line(s) between list items per WP:LISTGAP to fix an accessibility issue for users of screen readers. Do WP:GENFIXES and cleanup if needed. Discuss this at Wikipedia talk:WikiProject Accessibility#LISTGAP |
→The parameter \alpha: WP:SECTIONHEAD: For technical reasons, section headings should not contain <math> markup. (I don't know if this is the preferred way of fixing this. If not, feel free to improve this further!) |
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</math>
where <math>\kappa\vdash k</math> means <math>\kappa</math> is a [[partition (number theory)|partition]] of <math>k</math>, <math>(a_i)^{(\alpha )}_{\kappa}</math> is the [[
<math>C_\kappa^{(\alpha )}(X)</math> is the "C" normalization of the [[Jack function]].
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Unlike other functions of matrix argument, such as the [[matrix exponential]], which are matrix-valued, the hypergeometric function of (one or two) matrix arguments is scalar-valued.
==The parameter
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 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.
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* [http://www-math.mit.edu/~plamen/software/mhgref.html Software for computing the hypergeometric function of a matrix argument] by Plamen Koev.
{{series (mathematics)}}
[[Category:Hypergeometric functions]]
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