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, ... (sequence A052129 in the OEIS). This sequence can be shown to have asymptotic behaviour as follows:[1]
Guillera and Sondow give a representation in terms of the derivative of the Lerch transcendent:
where ln is the natural logarithm and (z, s, q) is the Lerch transcendent.
Finally,