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In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1$, $|z_1|^p + |z_3|^r < 1\}$. We consider cases $p=6$, $q= r= 2$ and $p=q=r=2$. We also investigate the Lu Qi-Keng problem for $p=q=r=2$.
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참고문헌 (23)
참고문헌 신청
S. Bergman / 1936 / Zur Theorie von pseudokonformen Abbildungen / Mat. Sb. (N.S.) 1(43)(1):79~96
L. Bers / 1958 / Mathematical Aspects of Subsonic and Transonic Gas Dynamics / Wiley
H. P. Boas / 1996 / The Lu Qi-Keng conjecture fails generically / Proc. Amer. Math. Soc 124(7):2021~2027
H. P. Boas / 1999 / The Bergman kernel function: explicit formulas and zeroes / Proc. Amer. Math. Soc 127(3):805~811
Junesang Choi / 2011 / Decomposition formulas and integral representations for some Exton hypergeometric functions / 충청수학회지 24(4):745~758
L. Bers / 1958 / Mathematical Aspects of Subsonic and Transonic Gas Dynamics / Wiley
H. P. Boas / 1996 / The Lu Qi-Keng conjecture fails generically / Proc. Amer. Math. Soc 124(7):2021~2027
H. P. Boas / 1999 / The Bergman kernel function: explicit formulas and zeroes / Proc. Amer. Math. Soc 127(3):805~811
Junesang Choi / 2011 / Decomposition formulas and integral representations for some Exton hypergeometric functions / 충청수학회지 24(4):745~758
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