Somos' quadratic recurrence constant


In mathematics, Somos' quadratic recurrence constant, named after Michael Somos, is the number
This can be easily re-written into the far more quickly converging product representation
which can then be compactly represented in infinite-product form by:
The constant σ arises when studying the asymptotic behaviour of the sequence
with first few terms 1, 1, 2, 12, 576, 1658880.... This sequence can be shown to have asymptotic behaviour as follows:
Guillera and Sondow give a representation in terms of the derivative of the Lerch transcendent:
where ln is the natural logarithm and is the Lerch transcendent.
Finally,