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,
The Somos' quadratic recurrence constant is named after Michael Somos, who is a researcher in the Georgetown University Mathematics Department on the third floor of the St. Mary's building.
[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).