The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a special limiting case as $p\to 0$. The elliptic beta integral of type $BC_1$ by van Diejen and Spiridonov is effectively used in the proof of the evaluation formula.

中文翻译：

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G2 型 Gustafson q 积分的椭圆扩展

证明了$G_2$型椭圆β积分的求值公式。积分由 Ruijsenaars 的椭圆伽马函数的乘积表示，公式包括类型为 $G_2$ 的 Gustafson 的 $q$-beta 积分作为 $p\to 0$ 的特殊极限情况。van Diejen 和 Spiridonov 的 $BC_1$ 类型的椭圆贝塔积分有效地用于评估公式的证明。