recipe for the construction of novel infinite products

1. Choose a special function that has limit zero. Airy functions work.
2. Compute \prod_{n=1}^{\infty} \left(1+\mathrm{Ai}(n)\right) \approx 1.1839521034335512376\ldots
3. See if you can eke any new identities out of it.

If a special function goes to infinity, its reciprocal goes to zero. Take the hyperfactorial H(n) = \prod_{k=1}^{n} k^{k}. You can then consider \prod_{n=1}^{\infty} \left(1 + \frac{1}{H(n)}\right)\approx 2.52323943705157931311\ldots

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One response to “recipe for the construction of novel infinite products

  1. I’ve started my math blog. It’s at futurebird.com… Nothing big there yet, but my goal is to write every day.

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