The product of all natural numbers

Calculus Level 4

Let \( x \) denote the product of all natural numbers (excluding zero).

\( x = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times \ldots \)

This is a divergent product. Using zeta function regularization, find the value of \( x \).

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