@article{Al-Hashami_2020, title={ Berezin-Karpelevich formula for chi-spherical functions on complex Grassmannians}, volume={50}, url={https://nzjmath.org/index.php/NZJMATH/article/view/62}, DOI={10.53733/62}, abstractNote={<p>In [5], Berezin and Karpelevich gave, without a proof, an explicit formula for spherical functions on complex Grassmannian manifolds. A first attempt to give a proof of Berezin-Karpelevich formula was taken, in [16], by Takahashi. His proof contained a gap, which was fixed later, in [10], by Hoogenboom. The aim of this paper is to generalize Berezin-Karpelevich formula to the case of $\chi$-spherical functions on complex Grassmannian manifolds $ SU(p+q)/S\left(U(p)\times U(q)\right)$.</p>}, journal={New Zealand Journal of Mathematics}, author={Al-Hashami, Mahmoud}, year={2020}, month={Nov.}, pages={29–48} }