Somos' quadratic recurrence constant

In mathematics, Somo's quadratic recurrence constant is defined as the number

$\sigma ={\sqrt {1{\sqrt {2{\sqrt {3\ldots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\ldots$

Sondow gives a representation in terms of the Lerch zeta function

xxx

and the series representation

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References

• S. Finch, Mathematical Constants, (2003) Cambridge University Press, Cambridge p.446
• Jesus Guillera and Jonathan Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent (2005) (Provides an integral and a series representation).