Somos' quadratic recurrence constant

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

This can be easily re-written into the far more quickly converging product representation

Sondow gives a representation in terms of the derivative of the Lerch transcendent:

where ln is the natural logarithm and Φ(z,s,q) is the Lerch transcendent.

A series representation, as a sum over the binomial coefficient, is also given:

Finally,

[edit] 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).