Harish-Chandra's Ξ function

In mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by Harish-Chandra (1966, section 16).

Harish-Chandra used it to define Harish-Chandra's Schwartz space.

Wallach (1988, 4.5) gives a detailed description of the properties of Ξ.

where

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