(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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#
series

# Integrating over simplices, and the Gamma function

# q-Powerseries and binary strings

(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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Consider the infinite product , and write this as . Relate to the binary expression of . The sequence starts off as: .