(Polya, Szego, Problems and Theorems in Analysis). Pick a sequence of positive numbers, , and set . Now write . Show that

where and is the canonical -dimensional simplex. In fact, the limit is .

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#
integration

# Integrating over simplices, and the Gamma function

(Polya, Szego, Problems and Theorems in Analysis). Pick a sequence of positive numbers, , and set . Now write . Show that

where and is the canonical -dimensional simplex. In fact, the limit is .

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