Zygmund (1988, p. 192) noted that there exists a number such that for each , the partial sums of the series are uniformly bounded below,
whereas for , they are not (Arias de Reyna and van de Lune
2009).
This constant is given by the unique solution for of
The origin of the defining property for appeared in an unpublished result of Littlewood and
Salem and the equation defining is due to S. Izumi (Zygmund 1988, p. 379),
thus justifying the name Littlewood-Salem-Izumi constant (Arias de Reyna and van
de Lune 2009).
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such that for each 
, the partial sums of the series 
are uniformly bounded below,
whereas for 
, they are not (Arias de Reyna and van de Lune
2009).
of
is a generalized hypergeometric
function, which is given by 
(OEIS A157957).
appeared in an unpublished result of Littlewood and
Salem and the equation defining 
is due to S. Izumi (Zygmund 1988, p. 379),
thus justifying the name Littlewood-Salem-Izumi constant (Arias de Reyna and van
de Lune 2009).
